Explore the relationships behind each calculator. Open a tool to see its variables and try a worked example.
Find a percentage of a number. Enter the number and percent to see the result, formula and calculation steps.
20% of 250 is 50.
Divide the percentage by 100 before multiplying.
Explore formula and calculator →Explore the area of a triangle, step by step.
A base of 12 m and height of 8 m gives 48 m².
Use the perpendicular height, not the sloping side.
Explore formula and calculator →Calculate compound growth from an initial amount, annual interest rate and time. See the formula and a worked example.
10,000 at 7% for 5 years grows to 14,025.52.
This assumes annual compounding, a fixed rate, and no fees or tax.
Explore formula and calculator →Calculate interest on a fixed principal.
10,000 at 5% for 2 years earns 1,000.
The result is interest only; it excludes the principal.
Explore formula and calculator →Find the area enclosed by a circle.
A radius of 5 m gives approximately 78.539816 m².
Radius is half the diameter.
Explore formula and calculator →Calculate average speed from distance and time.
120 km in 2 hours is an average of 60 km/h.
Use hours for time, not minutes.
Explore formula and calculator →Find voltage from current and resistance.
2 A through 12 Ω requires 24 V.
Applies to ideal ohmic components under constant physical conditions.
Explore formula and calculator →Estimate the volume of a rectangular slab.
5 m × 4 m × 0.15 m gives 3 m³.
Convert all dimensions to metres. Waste is not included.
Explore formula and calculator →Combine two values with their relative weights.
80 weighted at 40 and 90 weighted at 60 gives 86.
Weights are relative and do not need to add up to 100.
Explore formula and calculator →Find the final price after a discount.
15% off 1,000 gives a final price of 850.
Taxes and additional charges are excluded.
Explore formula and calculator →Convert metres to feet using the exact conversion factor of 0.3048 metres per foot. See the formula and worked steps.
1 metre is approximately 3.28084 feet.
Decimal feet are not feet and inches.
Explore formula and calculator →Convert Celsius to Fahrenheit. Enter the temperature in degrees Celsius and see the conversion formula, result and worked steps.
25 °C equals 77 °F.
Temperatures below absolute zero (−273.15 °C) are invalid.
Explore formula and calculator →Turn a rational number into its decimal value.
7/8 = 0.875.
A zero denominator is undefined. The displayed decimal may be rounded.
Explore formula and calculator →Find the principal square root of a non-negative number.
√144 = 12.
√n is the principal non-negative root. The equation x² = n can have two roots.
Explore formula and calculator →Evaluate integer powers, including negative exponents.
2⁵ = 32.
Negative exponents mean reciprocals. This tool rejects 0⁰ and zero to a negative power.
Explore formula and calculator →Substitute a value into a linear polynomial.
For p(x) = 3x + 2, p(4) = 14.
Multiply a by x before adding b. If a = 0, the polynomial is constant.
Explore formula and calculator →Find the x-value at which a linear polynomial is zero.
3x − 12 has its zero at x = 4.
A constant polynomial has either no zeros or infinitely many zeros; this tool requires a ≠ 0.
Explore formula and calculator →Watch a familiar algebraic identity become a number.
(10 + 3)² = 100 + 60 + 9 = 169.
Do not omit the middle term 2ab.
Explore formula and calculator →Evaluate a difference using its factorized form.
12² − 7² = 5 × 19 = 95.
This identity is for a difference of squares, not a sum.
Explore formula and calculator →Find any term of a sequence with a constant difference.
3, 7, 11, … has its 10th term at 39.
The first term is n = 1, so use n − 1 differences.
Explore formula and calculator →Find a term in a sequence with a constant ratio.
2, 6, 18, … has its 5th term at 162.
Multiply by the ratio n − 1 times. Extremely large sequences may exceed numeric limits.
Explore formula and calculator →Find the probability of an event with equally likely outcomes.
3 favourable outcomes out of 6 equally likely outcomes gives 0.5.
This counting formula assumes equally likely elementary outcomes.
Explore formula and calculator →Find a triangle’s area using its three sides.
Sides 3, 4, 5 cm give s = 6 cm and area = 6 cm².
The sides must form a non-degenerate triangle. Computation uses an equivalent stable form of Heron’s formula.
Explore formula and calculator →Calculate the area of a rectangle from its length and width. See the multiplication formula, input units and a worked example.
An 8 cm by 5 cm rectangle has an area of 40 cm².
Keep both dimensions in centimetres; area is measured in square centimetres.
Explore formula and calculator →Find the total length around a rectangle.
An 8 cm by 5 cm rectangle has a perimeter of 26 cm.
Perimeter is a length, not an area.
Explore formula and calculator →Measure the area of a parallelogram.
Base 9 cm and perpendicular height 4 cm give 36 cm².
The slanted side is not the perpendicular height.
Explore formula and calculator →Calculate the circumference of a circle from its radius. See the formula using pi, input units and a worked example.
A radius of 3 cm gives a circumference of approximately 18.849556 cm.
Radius is half the diameter.
Explore formula and calculator →Find the area of a circular sector from its angle.
Radius 3 cm and central angle 60° give approximately 4.712389 cm².
Enter the angle in degrees, between 0° and 360°.
Explore formula and calculator →Find the length along a circular arc.
Radius 3 cm and angle 60° give an arc length of π cm.
Arc length follows the curve; it is not the straight chord.
Explore formula and calculator →Measure the straight-line distance on a coordinate plane.
The distance from (0, 0) to (6, 8) is 10 units.
Use the same scale on both coordinate axes.
Explore formula and calculator →Find both coordinates halfway between two points.
The midpoint of (0, 0) and (6, 8) is (3, 4).
Do not mix an x-coordinate with a y-coordinate.
Explore formula and calculator →Find the other angle in a linear pair.
The supplement of 65° is 115°.
Supplementary angles sum to 180°, not 90°.
Explore formula and calculator →Find a triangle’s missing interior angle.
50° and 60° leave a third angle of 70°.
Use interior angles of a non-degenerate Euclidean triangle.
Explore formula and calculator →Complete the interior angles of a convex quadrilateral.
90°, 80° and 100° leave a fourth angle of 90°.
This tool accepts convex quadrilaterals only.
Explore formula and calculator →Find a chord’s length from its distance to the centre.
Radius 3 cm and distance 1 cm give a chord approximately 5.656854 cm long.
The distance is perpendicular to the chord, measured from the circle’s centre. Equality gives a zero-length limiting chord.
Explore formula and calculator →Find the volume of a right circular cylinder.
Radius 3 cm and height 7 cm give 63π cm³.
Use perpendicular height and consistent centimetre units.
Explore formula and calculator →Find the curved surface and both circular ends together.
Radius 3 cm and height 7 cm give a total surface area of 60π cm².
This is a closed cylinder, including both ends.
Explore formula and calculator →Find the volume of a right circular cone.
Radius 3 cm and height 7 cm give 21π cm³.
Use perpendicular height, not slant height.
Explore formula and calculator →Find the volume enclosed by a sphere.
A radius of 3 cm gives a volume of 36π cm³.
Enter radius, not diameter.
Explore formula and calculator →Find the volume of a rectangular solid.
8 cm × 5 cm × 3 cm gives 120 cm³.
All three dimensions must use the same unit.
Explore formula and calculator →Calculate the arithmetic mean of a list of numbers. See the sum, number of observations and division steps.
4, 8, 6, 10, 2 have a mean of 6.
Enter up to 200 numbers, separated by commas or spaces. All observations have equal weight.
Explore formula and calculator →Find the middle of an ordered ungrouped data set.
4, 8, 6, 10, 2 sort to 2, 4, 6, 8, 10; the median is 6.
Always sort the values first. For an even count, average the middle two.
Explore formula and calculator →Measure the spread between the smallest and largest values.
4, 8, 6, 10, 2 have a range of 10 − 2 = 8.
Range is sensitive to extreme values; it does not describe the complete distribution.
Explore formula and calculator →Solve add two fractions with your values and follow each calculation step.
1/3 + 1/6 = 3/6 = 1/2.
Add numerators only after using a common denominator. Denominators may be negative, but never zero.
Explore formula and calculator →Solve hcf / greatest common divisor with your values and follow each calculation step.
The HCF of 375 and 825 is 75.
Inputs must be positive whole numbers. Every displayed division is computed from your inputs.
Explore formula and calculator →Solve lowest common multiple with your values and follow each calculation step.
The LCM of 12 and 18 is 36.
Use positive whole numbers. LCM is a multiple, while HCF is a divisor.
Explore formula and calculator →Solve square of a difference with your values and follow each calculation step.
(5−2)² = 25−20+4 = 9.
The middle term is negative; the last term is positive.
Explore formula and calculator →Solve cube of a sum with your values and follow each calculation step.
(5+2)³ = 125+150+60+8 = 343.
A cube of a sum includes two middle terms.
Explore formula and calculator →Solve cube of a difference with your values and follow each calculation step.
(5−2)³ = 125−150+60−8 = 27.
The four signs are plus, minus, plus, minus.
Explore formula and calculator →Solve sum of cubes with your values and follow each calculation step.
5³+2³ = 7×19 = 133.
The middle sign in the quadratic factor is negative.
Explore formula and calculator →Solve difference of cubes with your values and follow each calculation step.
5³−2³ = 3×39 = 117.
Both signs inside the quadratic factor are positive.
Explore formula and calculator →Solve square of three terms with your values and follow each calculation step.
(5+2+3)² = 25+4+9+20+12+30 = 100.
There are three different cross-products; include each one twice.
Explore formula and calculator →Solve linear equation in one variable with your values and follow each calculation step.
3x+4=19 gives x=5.
Apply the same operation to both sides. This tool requires a unique solution.
Explore formula and calculator →Solve pair of linear equations with your values and follow each calculation step.
x+y=5 and x−y=1 give x=3, y=2.
Both equations use right-side constants. A unique intersection is required. Displayed intermediate decimals are rounded.
Explore formula and calculator →Solve slope of a line with your values and follow each calculation step.
From (1,2) to (5,10), slope = 8/4 = 2.
Use the same order of points in the numerator and denominator.
Explore formula and calculator →Solve sum of the first n natural numbers with your values and follow each calculation step.
1+2+…+100 = 5050.
This sums the integers starting at 1, with no missing terms.
Explore formula and calculator →Solve triangle perimeter with your values and follow each calculation step.
Sides 3,4,5 cm give a perimeter of 12 cm.
Three arbitrary lengths do not always form a triangle.
Explore formula and calculator →Solve equilateral triangle area with your values and follow each calculation step.
A side of 4 cm gives 4√3 ≈ 6.928203 cm².
All three sides must be equal.
Explore formula and calculator →Solve trapezium area with your values and follow each calculation step.
Parallel sides 6 and 10 cm with height 4 cm give 32 cm².
The two entered sides must be parallel.
Explore formula and calculator →Solve rhombus area from diagonals with your values and follow each calculation step.
Diagonals 6 and 8 cm enclose 24 cm².
Use the full lengths of both diagonals.
Explore formula and calculator →Solve brahmagupta’s formula with your values and follow each calculation step.
A cyclic quadrilateral with consecutive sides 3,4,3,4 cm has area 12 cm².
This formula requires a cyclic quadrilateral. Side lengths alone do not verify that your drawn quadrilateral is cyclic.
Explore formula and calculator →Solve sector perimeter with your values and follow each calculation step.
A quarter-sector of radius 7 cm has perimeter 14 + 3.5π cm.
Both radii form part of the boundary. Use a sector angle strictly between 0° and 360°.
Explore formula and calculator →Solve cube volume with your values and follow each calculation step.
A 4 cm cube encloses 64 cm³.
All three dimensions of a cube are equal.
Explore formula and calculator →Solve cube total surface area with your values and follow each calculation step.
A 4 cm cube has a total surface area of 96 cm².
This includes all six faces, not only the sides.
Explore formula and calculator →Solve cuboid total surface area with your values and follow each calculation step.
An 8×5×3 cm cuboid has total surface area 158 cm².
This includes every face of a closed cuboid.
Explore formula and calculator →Solve cylinder curved surface area with your values and follow each calculation step.
Radius 7 cm and height 12 cm give 168π cm².
The two circular ends are excluded.
Explore formula and calculator →Solve cone slant height with your values and follow each calculation step.
Radius 3 cm and perpendicular height 4 cm give slant height 5 cm.
Slant height and perpendicular height are different.
Explore formula and calculator →Solve cone curved surface area with your values and follow each calculation step.
Radius 3 cm and height 4 cm give 15π cm².
This excludes the circular base.
Explore formula and calculator →Solve cone total surface area with your values and follow each calculation step.
Radius 3 cm and height 4 cm give 24π cm².
The base is included. Enter the perpendicular height.
Explore formula and calculator →Solve sphere surface area with your values and follow each calculation step.
A sphere of radius 7 cm has surface area 196π cm².
Use radius, not diameter.
Explore formula and calculator →Solve hemisphere volume with your values and follow each calculation step.
A hemisphere of radius 7 cm encloses 686π/3 cm³.
A hemisphere is half of a sphere through its centre.
Explore formula and calculator →Solve hemisphere curved surface area with your values and follow each calculation step.
Radius 7 cm gives curved surface area 98π cm².
The flat circular base is excluded.
Explore formula and calculator →Solve hemisphere total surface area with your values and follow each calculation step.
Radius 7 cm gives total surface area 147π cm².
The flat circular base is included.
Explore formula and calculator →Solve pyramid volume with your values and follow each calculation step.
Base area 36 cm² and height 9 cm give 108 cm³.
The input is an area, not a base side length.
Explore formula and calculator →Calculate addition and see the working behind your result.
24 + 8 = 32.
Line up decimal places when adding decimals.
Explore formula and calculator →Calculate subtraction and see the working behind your result.
24 − 8 = 16.
The order matters; subtraction can give a negative answer.
Explore formula and calculator →Calculate multiplication and see the working behind your result.
24 × 8 = 192.
A negative number times a negative number is positive.
Explore formula and calculator →Calculate division and see the working behind your result.
24 ÷ 8 = 3.
The divisor cannot be zero.
Explore formula and calculator →Calculate division with remainder and see the working behind your result.
29 ÷ 6 gives quotient 4 and remainder 5.
The remainder must be smaller than the positive divisor.
Explore formula and calculator →Calculate place-value digit and see the working behind your result.
The hundreds digit of 5342 is 3.
Place 0 means ones; place 2 means hundreds.
Explore formula and calculator →Calculate multiply fractions and see the working behind your result.
2/3 × 3/5 = 6/15 = 0.4.
Both denominators must be positive. The final result is displayed as a decimal.
Explore formula and calculator →Calculate divide fractions and see the working behind your result.
2/3 ÷ 4/5 = 10/12 ≈ 0.833333.
The second fraction must not be zero.
Explore formula and calculator →Calculate share in a ratio and see the working behind your result.
Share 120 in the ratio 2:3: the two shares are 48 and 72.
This is a two-part ratio. The shares add up to the total.
Explore formula and calculator →Calculate unit price and see the working behind your result.
240 for 8 units is 30 per unit.
Quantity must be positive; currency is the same as your cost input.
Explore formula and calculator →Calculate the percentage increase or decrease between an original value and a new value, with the formula and worked steps.
An increase from 80 to 100 is 25%.
A negative result indicates a decrease. The original value must be positive.
Explore formula and calculator →Calculate pythagorean hypotenuse and see the working behind your result.
Perpendicular legs 3 and 4 give hypotenuse 5.
This tool assumes a right angle between the two given sides.
Explore formula and calculator →Calculate quadratic equation · real roots and see the working behind your result.
x²−5x+6=0 has roots 2 and 3.
Numerical evaluation uses an equivalent stable root formula. Repeated roots are displayed twice.
Explore formula and calculator →Calculate sine · degrees and see the working behind your result.
sin(30°) = 0.5.
Enter degrees, not radians. Displayed decimals are rounded.
Explore formula and calculator →Calculate cosine · degrees and see the working behind your result.
cos(30°) ≈ 0.866025.
Enter degrees, not radians. Displayed decimals are rounded.
Explore formula and calculator →Calculate tangent · degrees and see the working behind your result.
tan(30°) ≈ 0.577350.
Enter degrees, not radians. Displayed decimals are rounded.
Explore formula and calculator →Calculate logarithm to a chosen base and see the working behind your result.
log₁₀(100) = 2.
The number and base must be positive; the base cannot be one.
Explore formula and calculator →Calculate combinations · ncr and see the working behind your result.
Choosing 3 objects from 10 gives 120 combinations.
Inputs are integers from 0 to 50. Exact integer arithmetic is used before conversion to a safe numeric result.
Explore formula and calculator →Calculate permutations · npr and see the working behind your result.
Filling 3 ordered positions from 10 objects gives 720 arrangements.
Order matters. The maximum n is 18 to retain exact safe integer results.
Explore formula and calculator →Calculate binomial probability and see the working behind your result.
Exactly 2 successes in 5 fair trials has probability 0.3125.
This is the probability of exactly r successes, not at least r.
Explore formula and calculator →Calculate conditional probability and see the working behind your result.
P(A∩B)=0.2 and P(B)=0.5 give P(A|B)=0.4.
P(B) must be positive.
Explore formula and calculator →Calculate 2 × 2 determinant and see the working behind your result.
The determinant of [[3,2],[1,4]] is 10.
This tool is restricted to a 2 × 2 real matrix.
Explore formula and calculator →Calculate dot product · 3d and see the working behind your result.
(1,2,3)·(4,5,6) = 32.
A dot product is a scalar, not another vector.
Explore formula and calculator →Calculate vector magnitude · 3d and see the working behind your result.
The magnitude of (2,3,6) is 7.
The magnitude is always non-negative.
Explore formula and calculator →Calculate polynomial derivative at a point and see the working behind your result.
For p(x)=x³, the derivative at x=2 is 12.
This evaluates the derivative of a real polynomial of degree at most three; it is not an arbitrary-expression algebra system.
Explore formula and calculator →Calculate definite integral · cubic polynomial and see the working behind your result.
∫ from 0 to 2 of x³ dx = 4.
The integral is signed. Reversing the bounds changes its sign. This tool covers degree at most three.
Explore formula and calculator →Calculate simpson’s rule · integral of sin(x) and see the working behind your result.
On [0,π] with 12 intervals, the approximation is 2.000052624341.
Numerical approximation for sin(x) only, with angles in radians. Displayed rows are rounded; computation retains unrounded values.
Explore formula and calculator →Calculate population variance and see the working behind your result.
For 2,4,4,4,5,5,7,9 the population variance is 4.
This uses N for a complete population, not N−1 for a sample.
Explore formula and calculator →Calculate population standard deviation and see the working behind your result.
For 2,4,4,4,5,5,7,9 the population standard deviation is 2.
A population is divided by N. Do not use this as the sample standard deviation.
Explore formula and calculator →Calculate exponential differential equation and see the working behind your result.
y′=0.5y and y(0)=3 give y(2)=3e≈8.154845.
The rate k is constant; its inverse-time units must match the time input.
Explore formula and calculator →Canadian mortgage · semiannual compounding: use mortgage principal, nominal annual rate compounded semiannually, amortization period. Review the formula, worked example and calculation steps.
At 0%, a 120,000 mortgage over 10 years requires 1,000 monthly.
Fixed nominal annual rate compounded semiannually with monthly payments. The chosen amortization is not a guaranteed rate term. Excludes fees, insurance, taxes and prepayment rules; other Canadian products may use different conventions.
Explore formula and calculator →Calculate a fixed monthly loan payment from principal, annual interest and payment count. View the amortization schedule and calculation steps.
10,000 at 6% nominal annual interest over 36 months requires about 304.219375 per month.
Fixed nominal annual rate divided by 12; equal end-of-month payments. Excludes fees, insurance, taxes, variable rates and lender rounding.
Explore formula and calculator →Estimate monthly mortgage costs from price, down payment, rate, term, property tax and insurance. Review the assumptions and worked example.
250,000 price, 50,000 down, 6%, 30 years, 2,400 annual tax and 1,200 insurance gives about 1,499.101050 monthly.
Fixed nominal annual rate divided by 12; equal end-of-month payments. Excludes fees, insurance, taxes, variable rates and lender rounding. Property tax and insurance are supplied estimates; PMI and HOA charges are excluded.
Explore formula and calculator →Auto loan: use vehicle price, down payment, net trade-in credit. Review the formula, worked example and calculation steps.
25,000 price plus 1,000 fees, minus 5,000 down and 2,000 trade, finances 19,000.
Fixed nominal annual rate divided by 12; equal end-of-month payments. Excludes fees, insurance, taxes, variable rates and lender rounding. Enter the trade credit after any existing vehicle debt; enter taxes explicitly as financed fees.
Explore formula and calculator →Debt payoff with extra payments: use loan principal, nominal annual interest rate, number of monthly payments. Review the formula, worked example and calculation steps.
At zero interest, 1,200 over 12 months plus 100 extra monthly is repaid in 6 months.
Fixed nominal annual rate divided by 12; equal end-of-month payments. Excludes fees, insurance, taxes, variable rates and lender rounding. Extra payments are applied after the period’s interest. No prepayment penalties.
Explore formula and calculator →Credit card payoff · fixed payment: use current balance, nominal annual interest rate, fixed monthly payment. Review the formula, worked example and calculation steps.
A zero-interest 3,000 balance paid at 150 per month takes 20 months.
Monthly interest approximation with no new purchases, fees or changing minimum payment. Actual cards may compound daily.
Explore formula and calculator →Loan interest rate: use amount borrowed, monthly payment, number of monthly payments. Review the formula, worked example and calculation steps.
10,000 principal, 36 monthly payments of 304.2193745156 implies approximately 6% nominal annual interest.
Not a statutory APR calculation. No fees; supports non-negative monthly rates up to 100%.
Explore formula and calculator →APR estimate · monthly cash flows: use loan principal, nominal annual interest rate, number of monthly payments. Review the formula, worked example and calculation steps.
With no fees and 0% interest the effective annual rate is 0%.
An effective-rate cash-flow estimate, not the regulated APR disclosed under any country’s lending rules. Assumes equally spaced monthly payments.
Explore formula and calculator →Refinance break-even: use remaining principal, current nominal annual rate, new nominal annual rate. Review the formula, worked example and calculation steps.
With no refinancing costs and a lower rate, the payment-savings break-even is immediate.
Compares the same remaining term, principal and fixed monthly payment model. Excludes changes in tax, insurance and the time value of upfront costs.
Explore formula and calculator →Savings & investment growth: use initial balance, end-of-month deposit, nominal annual return. Review the formula, worked example and calculation steps.
1,000 initially plus 100 monthly at zero return for 12 months becomes 2,200.
Constant nominal annual return with monthly compounding and end-of-month deposits. No tax, fees or investment risk is modelled.
Explore formula and calculator →Savings goal · monthly deposit: use initial balance, target balance, nominal annual return. Review the formula, worked example and calculation steps.
From 1,000 to 2,200 in 12 months at 0% requires 100 per month.
Fixed hypothetical return and monthly compounding; deposits are at month end. No fees or taxes.
Explore formula and calculator →Retirement savings projection: use current savings, monthly contribution, nominal annual return. Review the formula, worked example and calculation steps.
50,000 plus 500 monthly for 30 years at 0% accumulates 230,000.
A savings projection, not a pension entitlement, 401(k), IRA or Social Security benefit estimator. No contribution limits, employer matching, tax or inflation.
Explore formula and calculator →Annuity payout · fixed term: use starting fund, nominal annual return, withdrawal period. Review the formula, worked example and calculation steps.
A 120,000 fund over 120 months at zero return permits 1,000 each month.
End-of-month fixed withdrawals with constant monthly compounding until the fund is exhausted. Not a lifetime insurance annuity; longevity, fees and tax are excluded.
Explore formula and calculator →Present value: use future lump sum, annual discount rate, time until payment. Review the formula, worked example and calculation steps.
110 due in one year discounted at 10% has present value 100.
Single lump sum, annual effective discount rate. No intermediate cash flows.
Explore formula and calculator →Inflation · future purchasing cost: use cost today, assumed annual inflation, years ahead. Review the formula, worked example and calculation steps.
1,000 with 10% inflation for 2 years becomes 1,210.
Uses your constant assumed rate; no historical CPI data or forecasts are fetched.
Explore formula and calculator →Currency converter · supplied rate: use amount in source currency, destination units per source unit. Review the formula, worked example and calculation steps.
100 source units at a supplied rate of 83 gives 8,300 destination units.
Supply a current rate from your provider. No live exchange-rate feed, fees or bid/ask spread.
Explore formula and calculator →Convert hourly pay to annual pay using paid hours per week and paid weeks per year. See the formula and assumptions.
20 per hour, 40 hours per week, 52 paid weeks gives 41,600 per year.
Gross pay before taxes and deductions. Enter only paid time; overtime premiums are not calculated.
Explore formula and calculator →Sales tax & VAT: use net price before tax, tax rate, calculation. Review the formula, worked example and calculation steps.
100 net at 18% tax becomes 118 gross; removing 18% from 118 returns 100.
This applies one supplied tax rate. It does not determine legal rates, exemptions or jurisdiction-specific rounding.
Explore formula and calculator →Profit margin & markup: use unit cost, selling price. Review the formula, worked example and calculation steps.
Cost 60 and selling price 100 gives 40% margin and 66.666667% markup.
Margin divides by revenue; markup divides by cost. Includes only the costs you entered.
Explore formula and calculator →Sales commission: use sales amount, commission rate. Review the formula, worked example and calculation steps.
10,000 sales at 5% gives 500 commission.
Single flat rate, before tax. No tiers, returns or clawbacks.
Explore formula and calculator →Debt-to-income ratio: use monthly debt payments, gross monthly income. Review the formula, worked example and calculation steps.
1,200 debt payments and 4,000 gross monthly income gives 30%.
Use gross income consistently. Lender definitions and approval thresholds vary; this is not a borrowing decision.
Explore formula and calculator →Monthly budget: use monthly take-home income, housing and utilities, food and household. Review the formula, worked example and calculation steps.
4,000 income minus 3,000 total allocations leaves 1,000.
All inputs must cover the same monthly period. A negative result means allocations exceed income.
Explore formula and calculator →Return on investment: use initial investment, final value including distributions. Review the formula, worked example and calculation steps.
1,000 invested and 1,200 returned gives 20% ROI.
Not annualized; include distributions and fees consistently. No intervening cash-flow timing.
Explore formula and calculator →Annualized investment return: use initial value, final value, holding period. Review the formula, worked example and calculation steps.
1,000 growing to 1,210 over two years gives 10% per year.
Assumes no intermediate contributions or withdrawals; this is a geometric return, not an arithmetic average.
Explore formula and calculator →Average periodic return: use periodic returns in percent. Review the formula, worked example and calculation steps.
10%, −10%, 20% has arithmetic average 6.666667%.
Use equally spaced periods. Arithmetic average differs from compound growth.
Explore formula and calculator →Net present value: use cash flows from time 0 onward, discount rate per period. Review the formula, worked example and calculation steps.
−1,000 today and 1,100 one period later at 10% discount gives NPV 0.
Regularly spaced cash flows. The supplied rate is per period, not necessarily per year.
Explore formula and calculator →Internal rate of return · conventional flows: use initial cost followed by periodic inflows. Review the formula, worked example and calculation steps.
−1,000 followed by 1,100 one period later gives IRR 10%.
Equal periods and one initial outflow only. Irregular dates, multiple sign changes and XIRR are not supported.
Explore formula and calculator →Payback period · constant cash flow: use initial investment, net inflow per period. Review the formula, worked example and calculation steps.
10,000 initial cost and 2,500 net inflow each year gives 4 years.
Undiscounted constant cash flow with fractional-period interpolation. Excludes cash flows after payback.
Explore formula and calculator →Bond price · fixed coupon: use face value, annual coupon rate, nominal annual yield. Review the formula, worked example and calculation steps.
A 1,000 face value bond with coupon rate equal to yield is priced at 1,000 on a coupon date.
Valuation exactly on a coupon date. Excludes accrued interest, default risk, embedded options and day-count conventions.
Explore formula and calculator →Straight-line depreciation: use asset cost, residual value, useful life. Review the formula, worked example and calculation steps.
10,000 cost, 1,000 residual and 5-year life gives 1,800 per year.
Straight-line accounting estimate, not jurisdiction-specific tax depreciation. No partial-year convention.
Explore formula and calculator →Auto lease · payment estimate: use adjusted capitalized cost, residual value, lease term. Review the formula, worked example and calculation steps.
30,000 capital, 18,000 residual, 36 months and 0.002 money factor gives 429.333333 before tax.
Use the monthly money factor, not an APR percentage. Excludes upfront charges and differing regional lease-tax rules.
Explore formula and calculator →Rental property · net yield: use property cost including acquisition fees, monthly rent, vacancy allowance. Review the formula, worked example and calculation steps.
200,000 cost, 1,500 monthly rent, 5% vacancy and 4,000 expenses gives 6.55%.
Unlevered operating yield; excludes finance, appreciation, sale costs and income tax.
Explore formula and calculator →Down payment: use purchase price, down-payment percentage. Review the formula, worked example and calculation steps.
20% of a 250,000 purchase is 50,000 down, leaving 200,000 before fees.
Does not include closing costs, affordability or lending eligibility.
Explore formula and calculator →Housing affordability · supplied budget: use gross monthly income, maximum housing share, monthly property tax, insurance and dues. Review the formula, worked example and calculation steps.
At 0%, a 1,000 monthly payment over 120 months supports a 120,000 loan before adding a down payment.
Your supplied budget percentage is a scenario assumption, not an underwriting recommendation. Excludes other debt tests, closing costs and loan insurance.
Explore formula and calculator →Debt consolidation · payment comparison: use current debt balances, corresponding nominal annual rates in percent, new consolidation nominal annual rate. Review the formula, worked example and calculation steps.
Two zero-interest balances totalling 5,000 over 10 months with no fees require 500 monthly.
Compares fixed rates over the same chosen term. Actual current debts may have different terms, minimum payments or early repayment fees.
Explore formula and calculator →College cost projection: use current annual study cost, annual cost inflation, years until study begins. Review the formula, worked example and calculation steps.
20,000 per year for 4 years at 0% inflation totals 80,000.
Constant supplied inflation; no grants, loans, taxes, investment growth or mid-year changes.
Explore formula and calculator →Long division · whole numbers: use dividend, divisor. Review the formula, worked example and calculation steps.
1248 ÷ 12 gives quotient 104 and remainder 0.
Non-negative whole-number dividend and positive divisor. Leading zero quotient digits are omitted from the headline but retained in the digit-by-digit working.
Explore formula and calculator →Evaluate expressions with trigonometry, roots, powers, logs and factorials. Use degree or radian mode and follow the worked steps.
sqrt(81) + 2^3 = 17.
Functions: sqrt, cbrt, root(degree, value), abs, ln, log (base 10), exp, sin, cos, tan, asin, acos and atan. Constants: pi and e. Use * for multiplication. Powers associate rightward; −2^2 is −4. Percent means divide by 100.
Explore formula and calculator →Fraction arithmetic: use first numerator, first denominator, operation. Review the formula, worked example and calculation steps.
1/2 + 1/3 = 5/6 ≈ 0.833333.
Whole-number numerators and positive denominators. The steps show the exact reduced fraction; the headline shows a rounded decimal.
Explore formula and calculator →Percent error: use observed value, reference value. Review the formula, worked example and calculation steps.
48 observed compared with 50 reference gives 4% error.
Uses an absolute reference magnitude; the error is non-negative.
Explore formula and calculator →Nth root · real numbers: use radicand, root degree. Review the formula, worked example and calculation steps.
The real cube root of −27 is −3.
Positive integer root degree. Complex roots are outside this tool’s scope.
Explore formula and calculator →Radioactive half-life: use initial quantity, elapsed time, half-life in the same time units. Review the formula, worked example and calculation steps.
100 units after 20 time units with a half-life of 10 leaves 25.
Single exponential decay without new production or daughter-product accumulation. Use consistent time units.
Explore formula and calculator →Z-score: use observed value, population mean, population standard deviation. Review the formula, worked example and calculation steps.
130 with mean 100 and standard deviation 15 gives z=2.
The standard deviation must be positive. A z-score alone does not imply a normal distribution.
Explore formula and calculator →P-value · standard normal z test: use z test statistic, alternative hypothesis. Review the formula, worked example and calculation steps.
z=1.96 gives a two-sided p-value of approximately 0.049996.
Normal z tests only; not Student t, chi-square, F or exact tests. Tail approximation can have absolute error around 10⁻⁷; very small p-values may display as zero.
Explore formula and calculator →Confidence interval · known population deviation: use sample mean, known population standard deviation, sample size. Review the formula, worked example and calculation steps.
Mean 100, known σ=15, n=100 and 95% confidence gives approximately 97.060054 to 102.939946.
Requires independent observations and normal sampling distribution (or an appropriate large-sample approximation). Known population σ only; use a t interval when estimating σ from a small sample.
Explore formula and calculator →Sample size · population proportion: use confidence level, margin of error, expected population proportion. Review the formula, worked example and calculation steps.
95% confidence, 5 percentage points margin and p=0.5 needs 385 observations for a large population.
Simple random sample for a proportion; no non-response or cluster-design adjustment. Normal approximation may be unsuitable for rare events or very small populations.
Explore formula and calculator →Sample standard deviation: use sample values. Review the formula, worked example and calculation steps.
For 2,4,4,4,5,5,7,9, sample standard deviation is approximately 2.13809.
Divides by n−1 for a sample, unlike the population standard deviation.
Explore formula and calculator →Mean, median, modes & range: use data values. Review the formula, worked example and calculation steps.
2,4,4,6 has mean 4, median 4, mode 4 and range 4.
All tied most-frequent values are shown. If every value occurs once, the result says no mode.
Explore formula and calculator →Factor & common factor finder: use first positive integer, second positive integer. Review the formula, worked example and calculation steps.
36 and 48 have common positive factors 1,2,3,4,6,12.
Positive whole numbers up to one billion. Zero has infinitely many divisors and is excluded.
Explore formula and calculator →Prime factorization: use positive integer. Review the formula, worked example and calculation steps.
360 = 2 × 2 × 2 × 3 × 3 × 5.
Integer input from 2 to 10¹²; uses exact safe-integer trial division.
Explore formula and calculator →Decimal rounding: use number, decimal places. Review the formula, worked example and calculation steps.
1234.56789 to 2 decimal places gives 1234.57; to −2 places gives 1200.
Nearest rounding; exact half ties go toward positive infinity. Binary floating-point can affect decimal ties. Display is limited to six decimal places even if more are retained.
Explore formula and calculator →Scientific notation: use finite number, significant figures. Review the formula, worked example and calculation steps.
123456 to 6 significant figures is 1.23456e+5.
Exponential notation uses e for powers of ten, not Euler’s constant. The source number is stored as a JavaScript floating-point value.
Explore formula and calculator →Binary, hexadecimal & big integer arithmetic: use first integer, second integer, input number base. Review the formula, worked example and calculation steps.
Hexadecimal FF + 1 = 100; decimal 255 + 1 = 256.
Up to 250 digits per input. No fractional digits or prefixes such as 0x. Integer division truncates toward zero; results retain exact BigInt precision.
Explore formula and calculator →Right triangle · sides & angles: use first perpendicular leg, second perpendicular leg. Review the formula, worked example and calculation steps.
Legs 3 and 4 give hypotenuse 5 and acute angles approximately 36.869898° and 53.130102°.
The two supplied sides must meet at a right angle. Angles are in degrees.
Explore formula and calculator →2 × 2 matrix arithmetic: use first matrix · row 1, column 1, first matrix · row 1, column 2, first matrix · row 2, column 1. Review the formula, worked example and calculation steps.
[[1,2],[3,4]] × [[5,6],[7,8]] = [[19,22],[43,50]].
Real 2×2 matrices only. Matrix multiplication is row-by-column and generally not commutative.
Explore formula and calculator →Calculate age between a date of birth and a chosen date. See the calendar-based result, calculation steps and date assumptions.
Born 2000-06-15, on 2026-11-02 the age is 26 completed years.
Gregorian calendar, date-only calculation. For February 29 births this uses March 1 as the anniversary in non-leap years; legal conventions can differ.
Explore formula and calculator →Date difference & day counter: use start date, end date. Review the formula, worked example and calculation steps.
2026-01-01 to 2026-02-01 is 31 days.
The start date is excluded. Negative means the end precedes the start; daylight saving does not affect date-only subtraction.
Explore formula and calculator →Date calculator · add or subtract days: use start date, days to add · negative to subtract, count. Review the formula, worked example and calculation steps.
2026-01-01 plus 30 calendar days is 2026-01-31.
Gregorian calendar. Weekday mode excludes only weekends and does not know local holidays.
Explore formula and calculator →Day of the week: use calendar date. Review the formula, worked example and calculation steps.
2026-11-02 is a Monday.
Uses the proleptic Gregorian calendar. Historical local calendar transitions are not modelled.
Explore formula and calculator →Time calculator · add minutes: use starting time, minutes to add · negative to subtract. Review the formula, worked example and calculation steps.
22:30 + 150 minutes gives 01:00 on the following day.
24-hour clock arithmetic; no timezone or daylight-saving transition.
Explore formula and calculator →Hours worked & time card: use start time, end time, unpaid break. Review the formula, worked example and calculation steps.
09:00 to 17:30 minus a 30-minute break gives 8 paid hours.
One shift; following-day mode adds exactly 24 hours. Does not include overtime rules or daylight-saving changes.
Explore formula and calculator →Time duration · date and clock: use start date, start time, end date. Review the formula, worked example and calculation steps.
2026-01-01 09:00 to 2026-01-02 17:00 is 32 hours.
Naive civil-time arithmetic without daylight saving; negative results indicate reversed endpoints.
Explore formula and calculator →UTC time zone converter: use utc date, utc time, destination timezone. Review the formula, worked example and calculation steps.
2026-11-02 12:00 UTC is 17:30 in Asia/Kolkata.
Conversion starts in UTC, avoiding ambiguous local daylight-saving times. Accuracy depends on the runtime timezone database; local wall-clock-to-UTC conversion is not provided.
Explore formula and calculator →GPA · supplied grade points: use grade points for each course, corresponding course credits. Review the formula, worked example and calculation steps.
4,3,3.5 with credits 3,3,2 gives GPA 3.5.
Supply grade points according to your school’s scale. Letter conversion, retake policy and honours weighting vary by institution.
Explore formula and calculator →Final grade needed: use current average, final exam weight, desired course grade. Review the formula, worked example and calculation steps.
An 80% current average, 40% final weight and 85% target requires 92.5% on the final.
A result above 100% is unattainable without extra credit; below 0% means the target is already secured. Assumes all non-final work is complete.
Explore formula and calculator →Fuel cost: use journey distance, fuel consumption, fuel price. Review the formula, worked example and calculation steps.
500 km at 7 L/100 km and 100 per litre costs 3,500.
Average consumption and constant fuel price. Excludes tolls, maintenance and idling differences.
Explore formula and calculator →Fuel economy & gas mileage: use distance driven, fuel used. Review the formula, worked example and calculation steps.
500 km on 35 L is 14.285714 km/L or 7 L/100 km.
US gallons, not imperial gallons. Use actual distance and fuel consumption over the same period.
Explore formula and calculator →Tip & bill split: use bill before tip, tip percentage, people sharing equally. Review the formula, worked example and calculation steps.
100 bill plus 15% tip split between 2 people is 57.50 each.
Tip applies to the entered bill; include or exclude tax according to your preference. Rounded individual shares may leave a small remainder.
Explore formula and calculator →Running pace: use distance, elapsed time. Review the formula, worked example and calculation steps.
5 km in 30 minutes gives 6 min/km and 10 km/h.
Average pace only, not moving pace or a performance prediction.
Explore formula and calculator →Sleep time arithmetic: use wake-up time, planned hours in bed, additional minutes in bed. Review the formula, worked example and calculation steps.
Wake at 07:00 after 8 hours in bed means bedtime 23:00.
Clock arithmetic only. Time in bed differs from sleep duration; this does not predict sleep cycles or prescribe a sleep schedule.
Explore formula and calculator →Convert a value between compatible units. Select source and target units, then review the conversion factor and calculation steps.
1 metre equals approximately 3.28084 feet.
International feet, avoirdupois mass and US liquid gallons. Temperature uses an offset and has a separate converter.
Explore formula and calculator →Temperature · Celsius, Fahrenheit & Kelvin: use temperature, source scale, destination scale. Review the formula, worked example and calculation steps.
25°C is 77°F or 298.15 K.
Absolute temperatures only, not temperature differences. Values below absolute zero are rejected.
Explore formula and calculator →IPv4 subnet calculator: use ipv4 address, cidr prefix length. Review the formula, worked example and calculation steps.
192.168.1.130/24 belongs to 192.168.1.0/24, with mask 255.255.255.0 and 254 conventional usable hosts.
IPv4 only. /31 uses point-to-point semantics; /32 is a single host. Does not verify address allocation, routing or network security.
Explore formula and calculator →Roman numeral converter: use whole number. Review the formula, worked example and calculation steps.
2026 = MMXXVI.
Whole numbers from 1 to 3999. No zero, negative numbers or extended overbar notation; conversion is decimal to Roman.
Explore formula and calculator →Base64 text encoder / decoder: use text or padded base64, operation. Review the formula, worked example and calculation steps.
Hello encodes as SGVsbG8=.
Base64 is an encoding, not encryption. This tool handles UTF-8 text and standard padded Base64, not binary files or base64url. Input and output are not added to automatic history.
Explore formula and calculator →URL component encoder / decoder: use text or encoded component, operation. Review the formula, worked example and calculation steps.
hello world encodes as hello%20world.
For a component, not an entire URL. Decoding does not treat + as a space. Encoding is not encryption. Automatic history is disabled for this tool.
Explore formula and calculator →Bandwidth & download time: use file size, connection throughput. Review the formula, worked example and calculation steps.
1,000 MB over 100 Mbit/s takes at least 80 seconds.
Decimal MB (10⁶ bytes) and Mbit/s (10⁶ bits/s). Ideal constant throughput; excludes latency and protocol overhead.
Explore formula and calculator →GDP · expenditure approach: use consumption, investment, government spending. Review the formula, worked example and calculation steps.
C=1000, I=300, G=400, X=200, M=250 gives GDP 1650.
Inputs must use consistent currency units, period and price basis. This arithmetic tool does not retrieve national accounts data.
Explore formula and calculator →Square footage: use length, width. Review the formula, worked example and calculation steps.
12 ft by 10 ft is 120 ft².
Rectangular horizontal area only. Add separate rectangles for irregular spaces.
Explore formula and calculator →Tile quantity: use length, width, tile length. Review the formula, worked example and calculation steps.
5 m × 4 m with 0.6 m × 0.6 m tiles and 10% waste needs 62 tiles.
Area estimate without a cutting layout. Grout gaps, carton sizes, patterns and unusable offcuts are not modelled.
Explore formula and calculator →Mulch volume: use length, width, depth. Review the formula, worked example and calculation steps.
5 m × 4 m × 0.1 m plus 10% allowance is 2.2 m³.
Loose rectangular volume estimate. Compaction and bag coverage depend on product.
Explore formula and calculator →Gravel volume & mass: use length, width, depth. Review the formula, worked example and calculation steps.
2.2 m³ at a supplied 1,600 kg/m³ is 3,520 kg.
Supply measured bulk density for your aggregate. Moisture, grading and compaction affect mass.
Explore formula and calculator →Roof area · uniform pitch: use length, width, pitch rise per 12 horizontal units. Review the formula, worked example and calculation steps.
A flat 5 m × 4 m plan with no allowance has area 20 m².
Uniform pitch over the entire rectangular projected footprint. Include eaves in the plan dimensions. Complex valleys, dormers and different pitches need separate areas.
Explore formula and calculator →Stair geometry: use total vertical rise, maximum desired riser height, tread going. Review the formula, worked example and calculation steps.
2.8 m total rise, maximum 0.18 m riser and 0.28 m going gives 16 risers, 0.175 m each, and 4.2 m run.
Simple single flight ending at a landing. Not a code-compliance check; headroom, width, nosing, handrails and landings are excluded.
Explore formula and calculator →Density: use mass, volume. Review the formula, worked example and calculation steps.
10 kg occupying 2 m³ has density 5 kg/m³.
Use consistent mass and volume units. Bulk density differs from intrinsic material density.
Explore formula and calculator →Mass from density & volume: use density, volume. Review the formula, worked example and calculation steps.
1,000 kg/m³ over 2 m³ gives 2,000 kg.
Density is assumed uniform over the supplied volume.
Explore formula and calculator →Weight force: use mass, gravitational acceleration. Review the formula, worked example and calculation steps.
70 kg at standard gravity 9.80665 m/s² weighs 686.4655 N.
Weight is a force in newtons; mass is in kilograms. Gravity varies with location.
Explore formula and calculator →Horsepower from torque: use shaft torque, rotational speed. Review the formula, worked example and calculation steps.
100 N·m at 3,000 rpm produces approximately 42.129451 mechanical hp.
Mechanical horsepower, not metric PS. Does not estimate engine output from vehicle weight or acceleration.
Explore formula and calculator →Electricity use & cost: use appliance power, hours used per day, number of days. Review the formula, worked example and calculation steps.
1,000 W for 3 hours daily over 30 days uses 90 kWh; at 8 per kWh it costs 720.
Constant power and tariff; excludes standby changes, demand charges, taxes and tariff tiers.
Explore formula and calculator →Series & parallel resistance: use resistances in ohms, connection. Review the formula, worked example and calculation steps.
100 Ω and 200 Ω in parallel gives 66.666667 Ω.
Ideal positive resistors only; excludes tolerance, temperature, power ratings and impedance.
Explore formula and calculator →DC voltage drop: use dc current, one-way cable length, conductor cross-sectional area. Review the formula, worked example and calculation steps.
10 A, 20 m one-way, 2.5 mm² and 0.0175 Ω·mm²/m gives 2.8 V drop.
Two-conductor DC circuit at constant current; supply voltage is used only for the percentage. Not AC impedance, three-phase design or cable ampacity.
Explore formula and calculator →Molarity from mass: use solute mass, supplied molar mass, final solution volume. Review the formula, worked example and calculation steps.
5.844 g with molar mass 58.44 g/mol in 1 L of final solution gives 0.1 mol/L.
Use final solution volume, not solvent volume. Supply correct chemical form, hydration state, purity and molar mass.
Explore formula and calculator →Cooling power · BTU/h & watts: use power, source unit. Review the formula, worked example and calculation steps.
12,000 BTU/h is approximately 3,516.852842 W.
Power conversion only, not a room heat-load or equipment-sizing recommendation.
Explore formula and calculator →Tire size geometry: use nominal section width, aspect ratio, rim diameter. Review the formula, worked example and calculation steps.
205/55 R16 gives nominal diameter 631.9 mm.
Nominal unloaded geometry. Manufacturer tolerances, load, inflation and tread wear change actual rolling dimensions; not a fitment approval.
Explore formula and calculator →Wind chill · NWS formula: use air temperature, wind speed. Review the formula, worked example and calculation steps.
0°F with a 15 mph wind gives wind chill approximately −19°F.
Defined for air temperature at or below 50°F and wind above 3 mph. Assumes shade; not the temperature of inanimate objects.
Explore formula and calculator →Dew point · liquid-water approximation: use air temperature, relative humidity. Review the formula, worked example and calculation steps.
25°C and 60% RH gives a dew point of approximately 16.705357°C.
Approximation using saturation over liquid water, restricted to −40 to 50°C and RH 1–100%. Below freezing, this is not the frost point.
Explore formula and calculator →Calculate adult BMI from weight and height for ages 20 and over. Review the formula and limitations; BMI alone does not diagnose health.
70 kg and 175 cm gives BMI 22.857143.
Adult screening measure only, not a diagnosis or individual health assessment. Not a child/teen percentile, pregnancy assessment or measure of body composition.
Explore formula and calculator →Adult BMI reference weight interval: use height, age. Review the formula, worked example and calculation steps.
At 175 cm, the adult BMI reference interval corresponds to 56.65625 kg to below 76.5625 kg.
Translates a population screening interval into weight; it is not an ideal-weight prescription, goal or nutritional plan. Individual context matters.
Explore formula and calculator →Resting energy expenditure · adult estimate: use weight, height, age. Review the formula, worked example and calculation steps.
70 kg, 175 cm, age 30 with the male equation gives 1,648.75 kcal/day.
Original study used adults aged 19–78. Resting expenditure is not total daily need or an intake target. Predictive equations have individual error and are not intended for children, pregnancy or clinical nutrition planning.
Explore formula and calculator →Daily energy · supplied activity factor: use weight, height, age. Review the formula, worked example and calculation steps.
A resting estimate of 1,648.75 multiplied by 1.2 gives 1,978.5 kcal/day.
The activity multiplier is your scenario input, not a measured or prescribed factor. No weight-loss target is generated. Not for children, pregnancy or clinical nutrition planning.
Explore formula and calculator →Macronutrients · supplied energy split: use energy amount to allocate, protein share, carbohydrate share. Review the formula, worked example and calculation steps.
2,000 kcal split 20/50/30 gives 100 g protein, 250 g carbohydrate and 66.666667 g fat.
Arithmetic using general 4/4/9 energy factors, not a recommended diet. User supplies energy and shares. Fibre, alcohol, food-specific energy factors and clinical needs are excluded.
Explore formula and calculator →Random integer generator: use minimum integer, maximum integer, how many integers. Review the formula, worked example and calculation steps.
Minimum 1 and maximum 6 generates a whole number from 1 to 6, inclusive.
Independent draws with replacement using platform cryptographic randomness. No weighted probabilities or sampling without replacement. A saved draw reopens with the original entropy; reset inputs to generate fresh draws.
Explore formula and calculator →Dice roller: use sides per die, number of dice. Review the formula, worked example and calculation steps.
Two six-sided dice produce a total from 2 to 12, with each die uniform.
Simulates fair independent dice with replacement. A saved roll reproduces the recorded result; reset inputs for fresh entropy.
Explore formula and calculator →Secure password generator: use password length, allowed characters. Review the formula, worked example and calculation steps.
A 20-character password drawn from 80 allowed symbols has about 126 bits of selection entropy.
No account is needed. Automatic history, in-app saving, input-sharing links and CSV export are disabled. Random selection does not guarantee every character class appears; use an appropriate password manager and follow the destination site’s rules.
Explore formula and calculator →Convert metric and imperial length units, including metres, centimetres, feet, inches and miles. Choose source and target units.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Weight & mass converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Energy converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
BTU uses the International Table definition; cal is a thermochemical calorie, not a food kilocalorie.
Explore formula and calculator →Power converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
hp and BHP use mechanical horsepower, not metric horsepower. TR is a refrigeration ton.
Explore formula and calculator →Voltage converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Current converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Apparent power converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Electric charge converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Frequency converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Angle converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Percent & parts per million converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
ppt means parts per trillion here. ppm is a ratio; conversion to mg/L also needs solution density.
Explore formula and calculator →Time units converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Area converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Volume units converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Speed converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Pressure converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Data storage converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Force converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Torque converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Density converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Acceleration converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Capacitance converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Resistance converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Volume flow rate converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Large number scale converter: use value, from, to. Review the formula, worked example and calculation steps.
Choose the source and destination units, then enter a value.
All conversions use the explicitly selected units. Negative values represent signed quantities where meaningful.
Explore formula and calculator →Sine calculator: use angle, angle unit. Review the formula, worked example and calculation steps.
sin(30 degrees) = 0.5.
Inverse functions return their principal values.
Explore formula and calculator →Cosine calculator: use angle, angle unit. Review the formula, worked example and calculation steps.
sin(30 degrees) = 0.5.
Inverse functions return their principal values.
Explore formula and calculator →Tangent calculator: use angle, angle unit. Review the formula, worked example and calculation steps.
sin(30 degrees) = 0.5.
Inverse functions return their principal values.
Explore formula and calculator →Arcsine calculator: use ratio, angle unit. Review the formula, worked example and calculation steps.
arcsin(0.5) = 30 degrees.
Inverse functions return their principal values.
Explore formula and calculator →Arccosine calculator: use ratio, angle unit. Review the formula, worked example and calculation steps.
sin(30 degrees) = 0.5.
Inverse functions return their principal values.
Explore formula and calculator →Arctangent calculator: use ratio, angle unit. Review the formula, worked example and calculation steps.
sin(30 degrees) = 0.5.
Inverse functions return their principal values.
Explore formula and calculator →Factorial: use nonnegative integer. Review the formula, worked example and calculation steps.
5! = 120.
Defined here for nonnegative integers only.
Explore formula and calculator →Natural logarithm: use positive number. Review the formula, worked example and calculation steps.
ln(e) = 1.
The real logarithm requires a positive argument.
Explore formula and calculator →Antilogarithm: use exponent, base. Review the formula, worked example and calculation steps.
The base-10 antilog of 2 is 100.
The base must be positive and different from 1.
Explore formula and calculator →Exponential growth & decay: use initial value, rate per time unit, elapsed time. Review the formula, worked example and calculation steps.
100 at 5% per period for 2 periods is 110.25.
Uses discrete compounding; time units must match the rate.
Explore formula and calculator →Complex numbers: use first real part, first imaginary part, second real part. Review the formula, worked example and calculation steps.
(1+2i)(3+4i) = −5+10i.
The imaginary unit satisfies i² = −1.
Explore formula and calculator →Discrete convolution: use first sequence, second sequence. Review the formula, worked example and calculation steps.
[1,2,3] convolved with [1,1] gives [1,3,5,3].
Finite discrete linear convolution, with index 0 at the first sample; not circular or continuous convolution.
Explore formula and calculator →Number base converter: use whole number, source base, target base. Review the formula, worked example and calculation steps.
FF in base 16 is 255 in base 10.
Whole numbers only; bases 2–36 use 0–9 and A–Z.
Explore formula and calculator →Decimal to fraction: use decimal value. Review the formula, worked example and calculation steps.
0.125 = 1/8.
Approximates the entered finite decimal; repeating decimals must be entered to sufficient precision.
Explore formula and calculator →Simplify fraction: use numerator, denominator. Review the formula, worked example and calculation steps.
12/18 = 2/3.
A negative sign is kept in the numerator.
Explore formula and calculator →Degrees ↔ degrees minutes seconds: use direction, degrees, minutes (to decimal only). Review the formula, worked example and calculation steps.
12.5° = 12° 30′ 0″.
For negative DMS values, put the negative sign on degrees.
Explore formula and calculator →Final grade calculator: use current grade, desired overall grade, final exam weight. Review the formula, worked example and calculation steps.
80% current, 40% final weight, and 85% target requires 92.5% on the final.
A result above 100% means the target is unattainable without extra credit.
Explore formula and calculator →Letter grade ↔ GPA: use direction, letter grade, gpa (reverse direction). Review the formula, worked example and calculation steps.
A = 4.0; B = 3.0; C = 2.0.
Schools use different mappings. This is a visible example scale, not an institutional policy. A+ and A both map to 4.0; reverse conversion chooses A+.
Explore formula and calculator →GST & VAT calculator: use amount, supplied tax rate, tax treatment. Review the formula, worked example and calculation steps.
100 plus 18% is 118; removing 18% from 118 gives 100.
Use the rate applicable to your transaction. No jurisdiction or current tax rate is inferred.
Explore formula and calculator →Weighted course grades: use scores as percentages, corresponding relative weights. Review the formula, worked example and calculation steps.
80,90,100 weighted at 20,30,50 gives 93%.
Weights are relative. All scores must use the same percentage scale.
Explore formula and calculator →Find a percent of a number, what percent one value is of another, or the original total from a part and percentage.
20% of 250 = 50; 50 is 20% of 250.
For increase/decrease, first is the percentage and second is the original amount. For change, first is original and second is new. Percentage change uses the magnitude of the original as its base.
Explore formula and calculator →Fraction, decimal & percent: use conversion, numerator / percentage, denominator (fraction input). Review the formula, worked example and calculation steps.
1/8 = 0.125 = 12.5%.
Percent-to-fraction uses a continued-fraction approximation with denominator at most 10⁹.
Explore formula and calculator →Ratio simplifier & proportion: use operation, first ratio · first term, first ratio · second term. Review the formula, worked example and calculation steps.
2:3 = 8:12. The ratio 12:18 simplifies to 2:3.
Simplification uses integer ratio terms. A ratio with a zero second term is not supported.
Explore formula and calculator →Compound interest · compounding periods: use principal, nominal annual interest, years. Review the formula, worked example and calculation steps.
1,000 at 12% nominal compounded monthly for 1 year grows to 1,126.82503.
Fixed rate, no contributions, taxes or fees. Fractional years use the same mathematical compounding model.
Explore formula and calculator →Effective annual interest rate: use nominal annual interest, compounding periods per year. Review the formula, worked example and calculation steps.
12% nominal compounded monthly gives an effective annual rate of approximately 12.682503%.
Compounding-only effective rate. This does not include fees or define a regulated loan APR.
Explore formula and calculator →Temperature · Celsius Fahrenheit Kelvin Rankine: use temperature, from, to. Review the formula, worked example and calculation steps.
0 K = 0 °R = −273.15 °C = −459.67 °F.
Absolute temperatures, not differences; Rankine uses Fahrenheit-sized degrees.
Explore formula and calculator →Custom unit conversion: use input value, multiplication factor, offset after multiplication. Review the formula, worked example and calculation steps.
Inches to cm: factor 2.54, offset 0. Celsius to Fahrenheit: factor 1.8, offset 32.
Supply the correct factor and offset. The tool does not infer or verify the units.
Explore formula and calculator →Fibonacci numbers: use index n (f₀ = 0, f₁ = 1). Review the formula, worked example and calculation steps.
F₁₀ = 55.
Uses zero-based indexing and exact integer arithmetic.
Explore formula and calculator →Amps to watts: use current, voltage, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Watts to amps: use real power, voltage, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Volts to watts: use voltage, current, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Watts to volts: use real power, current, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Amps to kW: use current, voltage, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →kW to amps: use real power, voltage, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Volts to kW: use voltage, current, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →kW to volts: use real power, current, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Amps to VA: use current, voltage, circuit. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →VA to amps: use apparent power, voltage, circuit. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →VA to watts: use apparent power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Watts to VA: use real power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →VA to kW: use apparent power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →kW to VA: use real power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Amps to KVA: use current, voltage, circuit. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →KVA to amps: use apparent power, voltage, circuit. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →KVA to watts: use apparent power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Watts to KVA: use real power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →KVA to kW: use apparent power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →kW to KVA: use real power, power factor. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Watts to Joules: use watts, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Watts to kJ: use watts, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Watts to Wh: use watts, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Watts to kWh: use watts, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kW to Joules: use kw, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kW to kJ: use kw, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kW to Wh: use kw, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kW to kWh: use kw, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Joules to Watts: use joules, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Joules to kW: use joules, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kJ to Watts: use kj, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kJ to kW: use kj, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Wh to Watts: use wh, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Wh to kW: use wh, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kWh to Watts: use kwh, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →kWh to kW: use kwh, duration. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Enter duration in hours. Energy and power are different physical quantities.
Explore formula and calculator →Volts to amps · resistance: use voltage, resistance. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Amps to volts · resistance: use current, resistance. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Amps to ohms: use current, voltage. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Ohms to amps: use resistance, voltage. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Ohms to volts: use resistance, current. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Volts to ohms: use voltage, current. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Voltage divider: use voltage, upper resistor r₁, lower resistor r₂. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal unloaded resistive divider. Loading and tolerances affect the actual voltage.
Explore formula and calculator →Power factor: use real power, apparent power. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Electricity bill estimate: use load, hours per day, days. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Constant load and flat supplied tariff. Tiered pricing, time-of-use rates, tax and demand charges are excluded.
Explore formula and calculator →Energy consumption: use power, hours per day, days. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Volts to joules: use voltage, charge. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Joules to volts: use energy, charge. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Volts to eV: use voltage, charge magnitude in elementary charges. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →eV to volts: use energy, charge magnitude in elementary charges. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Wh to mAh: use energy, voltage. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →mAh to Wh: use capacity, voltage. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Ideal steady-state calculation. Three-phase uses balanced loads and line-to-line RMS voltage.
Explore formula and calculator →Decibels · power & amplitude: use ratio, ratio type. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Amplitude comparisons assume equal impedances.
Explore formula and calculator →dBm ↔ power: use value, conversion. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Logarithmic conversions require strictly positive power.
Explore formula and calculator →Wire gauge · AWG & SWG: use gauge standard, gauge number (−1 = 2/0, −3 = 4/0). Review the formula, worked example and calculation steps.
AWG 12 diameter is approximately 2.0525 mm; SWG 12 is 2.6416 mm.
Gauge describes geometry, not allowable current. Insulation, conductor material, temperature, installation and local codes determine ratings.
Explore formula and calculator →Candela to lumens: use luminous intensity, full cone angle. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lumens to candela: use luminous flux, full cone angle. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lumens to millicandela: use luminous flux, full cone angle. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Millicandela to lumens: use luminous intensity, full cone angle. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Candela to lux: use luminous intensity, distance. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lux to candela: use illuminance, distance. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lumens to lux: use luminous flux, illuminated area. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lux to lumens: use illuminance, illuminated area. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Watts to lumens: use electrical power, luminous efficacy. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lumens to watts: use luminous flux, luminous efficacy. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Watts to lux: use electrical power, luminous efficacy, illuminated area. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lux to watts: use illuminance, luminous efficacy, illuminated area. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Footcandles to lux: use illuminance. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Lux to footcandles: use illuminance. Review the formula, worked example and calculation steps.
Change the supplied example values to match your circuit.
Uniform flux over the supplied area or cone. Distance assumes a point source and normal incidence. Supply the actual efficacy of your light.
Explore formula and calculator →Watts, volts, amps & ohms: use known quantities (first / second), first quantity, second quantity. Review the formula, worked example and calculation steps.
12 V and 2 A gives 6 Ω and 24 W.
Positive magnitudes for an ideal DC resistor. This is not an AC impedance or reactive-power model.
Explore formula and calculator →Height · feet and inches: use direction, centimetres (metric input), feet (imperial input). Review the formula, worked example and calculation steps.
5 ft 7 in = 170.18 cm.
The direction determines which input fields are used. Decimal feet are not feet plus inches.
Explore formula and calculator →ppm to mg/L: use mass concentration, solution density. Review the formula, worked example and calculation steps.
10 ppm by mass in a 1 kg/L solution equals 10 mg/L.
ppm and mg/L are numerically equal only at density 1 kg/L. Gas volume ratios need a different model.
Explore formula and calculator →Next birthday: use date of birth, from date, february 29 in non-leap years. Review the formula, worked example and calculation steps.
A June 15 birthday viewed on November 7, 2026 next occurs on June 15, 2027.
Uses date-only Gregorian arithmetic. Today’s birthday is counted as zero days away.
Explore formula and calculator →Date to Roman numerals: use date, date order. Review the formula, worked example and calculation steps.
2026-11-07 in day-month-year order is VII · XI · MMXXVI.
This changes date notation; it does not convert calendar systems.
Explore formula and calculator →Test grade: use total points or questions, points earned or correct answers. Review the formula, worked example and calculation steps.
17 correct out of 20 gives 85%.
Arithmetic score only; letter grades and pass thresholds depend on your institution.
Explore formula and calculator →Significant figures: use first measured number, second measured number (operations only), operation. Review the formula, worked example and calculation steps.
12.30 has 4 significant figures. 12.30 × 1.2 rounds to 15.
Trailing zeros in an integer without a decimal point are treated as placeholders. Use 1200. or scientific notation to state their significance.
Explore formula and calculator →Percentage difference: use first value, second value. Review the formula, worked example and calculation steps.
80 and 100 differ by approximately 22.2222% of their average.
Symmetric comparison of nonnegative values; both zero is defined here as zero difference. This is not directional percentage change.
Explore formula and calculator →Doubling time: use growth per period. Review the formula, worked example and calculation steps.
100% growth per period doubles in one period.
Constant discrete compound growth, not the approximate rule of 72.
Explore formula and calculator →Law of cosines: use side a, side b, included angle. Review the formula, worked example and calculation steps.
Sides 3 and 4 with a 90° included angle give side 5.
The angle is between the two known sides.
Explore formula and calculator →Law of sines: use known side a, opposite angle a, target angle b. Review the formula, worked example and calculation steps.
a=5 opposite 30°, B=90° gives b=10.
Solves a triangle with two known angles. It does not silently choose a branch in the ambiguous SSA case.
Explore formula and calculator →Ellipse area: use semimajor radius, semiminor radius. Review the formula, worked example and calculation steps.
Semiaxes 5 m and 3 m give 15π m².
Use semiaxes, which are half the full width and height.
Explore formula and calculator →Ellipse perimeter: use first semiaxis, second semiaxis. Review the formula, worked example and calculation steps.
A circle with both semiaxes 1 m gives 2π m.
A high-accuracy approximation for ellipses, not an exact elementary formula.
Explore formula and calculator →Regular polygon area: use number of sides, side length. Review the formula, worked example and calculation steps.
A regular square of side 2 has area 4.
Every side and every interior angle must be equal.
Explore formula and calculator →Polygon interior angle: use number of sides. Review the formula, worked example and calculation steps.
A regular hexagon has interior angle 120°.
This returns each interior angle of a regular convex polygon.
Explore formula and calculator →Annulus area: use outer radius, inner radius. Review the formula, worked example and calculation steps.
Radii 5 and 3 give 16π square units.
Both circles must share a centre.
Explore formula and calculator →Triangle area · two sides & angle: use side a, side b, included angle. Review the formula, worked example and calculation steps.
Sides 3 and 4 with included angle 90° give area 6.
Use the included angle, not another angle of the triangle.
Explore formula and calculator →Triangular prism volume: use triangle base, triangle perpendicular height, prism length. Review the formula, worked example and calculation steps.
3 × 4 / 2 × 5 = 30 m³.
Prism length is perpendicular to its triangular cross-section.
Explore formula and calculator →Conical frustum volume: use first radius, second radius, perpendicular height. Review the formula, worked example and calculation steps.
Radii 3 and 1, height 6 give 26π m³.
Radii refer to parallel circular ends; height is perpendicular, not the slant length.
Explore formula and calculator →Torus volume: use major radius to tube centre, tube radius. Review the formula, worked example and calculation steps.
Major radius 3 and tube radius 1 give 6π².
Ring torus geometry; the tube must not cross the central axis.
Explore formula and calculator →Spherical cap volume: use sphere radius, cap height. Review the formula, worked example and calculation steps.
R=3 and h=1 gives 8π/3.
Measure cap height from the cap plane to the pole of the sphere.
Explore formula and calculator →3D distance: use first x, first y, first z. Review the formula, worked example and calculation steps.
(0,0,0) to (1,2,2) has distance 3.
All coordinates must use the same Cartesian unit scale.
Explore formula and calculator →Vector cross product: use first vector · 3 components, second vector · 3 components. Review the formula, worked example and calculation steps.
(1,0,0) × (0,1,0) = (0,0,1).
Order matters: b×a = −(a×b).
Explore formula and calculator →Mode: use observations. Review the formula, worked example and calculation steps.
1,2,2,3,4 has mode 2.
Reports all tied modes. If every value occurs once, no repeated mode is reported.
Explore formula and calculator →Standard error of the mean: use observations. Review the formula, worked example and calculation steps.
For 1,2,3 the sample standard deviation is 1 and SE is 1/√3.
Assumes independent observations. Standard error is different from the spread of individual values.
Explore formula and calculator →Pearson correlation: use x observations, y observations. Review the formula, worked example and calculation steps.
X=1,2,3 and Y=2,4,6 have correlation 1.
A linear relationship summary, not proof of causation. Constant variables are rejected.
Explore formula and calculator →Linear regression: use x observations, y observations, x value for prediction. Review the formula, worked example and calculation steps.
X=1,2,3 and Y=2,4,6 predicts Y=8 at X=4.
Fits one predictor with an intercept; extrapolation beyond the observed range can be unreliable.
Explore formula and calculator →Covariance: use x observations, y observations, estimator. Review the formula, worked example and calculation steps.
Sample covariance of [1,2,3] and [2,4,6] is 2.
Covariance has combined units; its magnitude is not a normalized association measure.
Explore formula and calculator →Geometric mean: use observations. Review the formula, worked example and calculation steps.
The geometric mean of 2 and 8 is 4.
Uses positive observations; do not apply directly to signed percentage returns.
Explore formula and calculator →Harmonic mean: use observations. Review the formula, worked example and calculation steps.
For 3 and 6, the harmonic mean is 4.
The harmonic mean is useful for rates with equal numerator quantities, such as equal distances.
Explore formula and calculator →Coefficient of variation: use observations. Review the formula, worked example and calculation steps.
For 1,2,3, sample SD=1 and mean=2, so CV=50%.
Meaningful for ratio-scale data; undefined at zero mean and restricted here to positive means.
Explore formula and calculator →Weighted mean · data lists: use values, weights. Review the formula, worked example and calculation steps.
80,90,100 weighted by 2,3,5 gives 93.
Weights are relative and need not add up to 100.
Explore formula and calculator →Percentile: use observations, percentile. Review the formula, worked example and calculation steps.
The 75th percentile of 1,2,3,4,5 is 4.
Uses the inclusive linear interpolation convention; other software may use different percentile definitions.
Explore formula and calculator →Interquartile range: use observations. Review the formula, worked example and calculation steps.
1,2,3,4,5 has Q1=2, Q3=4, and IQR=2.
Quartile conventions vary; the convention is stated explicitly.
Explore formula and calculator →Outlier fences: use observations. Review the formula, worked example and calculation steps.
1,2,3,4,100 flags 100 using 1.5×IQR fences.
A screening convention, not a rule to automatically remove observations.
Explore formula and calculator →Expected value: use outcomes, probabilities. Review the formula, worked example and calculation steps.
80% chance of 0 and 20% chance of 10 gives expectation 2.
An expected value need not be an outcome that can occur on a single trial.
Explore formula and calculator →Normal distribution: use observation, mean, standard deviation. Review the formula, worked example and calculation steps.
At its mean, a normal distribution has CDF 0.5.
Normal model with supplied parameters; a density value is not a point probability. CDF approximation error is about 1.5×10⁻⁷ or less.
Explore formula and calculator →p-value · normal & Student t: use test statistic, null distribution, degrees of freedom (t only). Review the formula, worked example and calculation steps.
Student t=1 with 1 degree of freedom gives two-sided p=0.5.
Requires a valid test statistic and null model; not the probability that a hypothesis is true. Does not implement F or chi-square tails.
Explore formula and calculator →One-sample z test: use sample mean, null mean, known population standard deviation. Review the formula, worked example and calculation steps.
Mean105, null100, σ10, n25 gives z=2.5.
Assumes a known population SD and a justified normal sampling model.
Explore formula and calculator →Poisson probability: use expected count λ, observed count k. Review the formula, worked example and calculation steps.
λ=3 and k=2 gives approximately 0.224042.
Counts independent events with constant expected intensity over the interval.
Explore formula and calculator →Exponential distribution: use rate λ, elapsed quantity. Review the formula, worked example and calculation steps.
Rate0.5 and x2 gives 1−e⁻¹ ≈0.632121.
Nonnegative waiting-time model with constant hazard; rate units must match the inverse of x units.
Explore formula and calculator →Uniform distribution: use lower bound, upper bound, observation. Review the formula, worked example and calculation steps.
For U(0,10), P(X≤4)=0.4.
Continuous uniform distribution with constant density on the stated interval.
Explore formula and calculator →Relative frequency: use count for the category, total observations. Review the formula, worked example and calculation steps.
12 of 40 observations gives relative frequency0.3.
Use consistent counts; a frequency estimate is not necessarily the underlying probability.
Explore formula and calculator →Salary to hourly: use salary amount, salary period, working hours per week. Review the formula, worked example and calculation steps.
52,000 per year ÷ 40 hours ÷ 52 weeks gives 25 per hour.
Daily salary assumes five paid days per working week. Gross pay only; no taxes, benefits, overtime or unpaid leave is inferred.
Explore formula and calculator →Markup: use unit cost, selling price. Review the formula, worked example and calculation steps.
Cost80 and price100 gives markup25%.
Markup uses cost as its base; profit margin uses selling price.
Explore formula and calculator →Price from markup: use unit cost, markup. Review the formula, worked example and calculation steps.
80 with 25% markup gives a price of100.
Excludes tax, marketplace fees, shipping and other costs.
Explore formula and calculator →Break-even point: use fixed costs, selling price per unit, variable cost per unit. Review the formula, worked example and calculation steps.
Fixed costs1000 and contribution10 per unit require100 units.
Assumes constant unit price and cost with no capacity limits. Rounds up to whole units.
Explore formula and calculator →Compound annual growth rate: use starting value, ending value, years. Review the formula, worked example and calculation steps.
1000 growing to1210 in2 years has CAGR10%.
A smoothed annual growth rate; intermediate deposits, withdrawals and risk are not modelled.
Explore formula and calculator →Rule of 72: use annual growth rate. Review the formula, worked example and calculation steps.
At6%, the rule estimates12 years to double.
A rough mental approximation. Use Doubling time for the exact constant-rate discrete model.
Explore formula and calculator →Gross profit: use revenue, cost of goods sold. Review the formula, worked example and calculation steps.
Revenue10000 minus COGS6000 gives gross profit4000.
Operating expenses, tax and interest are excluded.
Explore formula and calculator →Net profit: use revenue, total expenses. Review the formula, worked example and calculation steps.
Revenue10000 minus expenses8500 gives profit1500.
Include every expense relevant to your accounting period; this tool does not infer accounting or tax rules.
Explore formula and calculator →Operating margin: use operating income, revenue. Review the formula, worked example and calculation steps.
Operating income1500 on revenue10000 gives15%.
Use operating income, not gross or net income.
Explore formula and calculator →Return on assets: use net income, average total assets. Review the formula, worked example and calculation steps.
Income20000 on average assets200000 gives10%.
Use matching periods and the appropriate accounting definition of assets.
Explore formula and calculator →Return on equity: use net income, average shareholder equity. Review the formula, worked example and calculation steps.
Income20000 and average equity100000 gives20%.
Restricted here to positive equity; negative-equity cases need separate interpretation.
Explore formula and calculator →Current ratio: use current assets, current liabilities. Review the formula, worked example and calculation steps.
Current assets20000 and liabilities10000 gives2.
A point-in-time liquidity ratio, not a prediction of cash availability.
Explore formula and calculator →Quick ratio: use cash & equivalents, marketable securities, net receivables. Review the formula, worked example and calculation steps.
Quick assets15000 and liabilities10000 gives1.5.
Excludes inventory and prepayments; classification and collectability matter.
Explore formula and calculator →Working capital: use current assets, current liabilities. Review the formula, worked example and calculation steps.
20000 minus10000 gives10000.
Uses current accounts, not all assets and liabilities.
Explore formula and calculator →Inventory turnover: use period cost of goods sold, average inventory at cost. Review the formula, worked example and calculation steps.
COGS120000 and average inventory20000 gives6 turns.
Use cost consistently in numerator and denominator.
Explore formula and calculator →Days sales outstanding: use average receivables, credit sales during period, days in period. Review the formula, worked example and calculation steps.
Receivables10000 on annual credit sales100000 gives36.5 days.
Seasonality and unusual sales patterns can distort this period-average estimate.
Explore formula and calculator →Earnings per share: use net income, preferred dividends, weighted average common shares. Review the formula, worked example and calculation steps.
(100000−10000)/10000 gives9 per share.
Basic EPS; dilution and detailed accounting adjustments are excluded.
Explore formula and calculator →Price to earnings ratio: use share price, earnings per share. Review the formula, worked example and calculation steps.
Price50 and EPS5 gives P/E10.
Requires positive EPS here. Use matching periods and definitions; this is arithmetic, not an investment recommendation.
Explore formula and calculator →Dividend yield: use annual dividend per share, share price. Review the formula, worked example and calculation steps.
Dividend2 on price50 gives4%.
A supplied dividend is not a promise of future distributions.
Explore formula and calculator →Discount factor: use discount rate per period, periods. Review the formula, worked example and calculation steps.
At10% over2 periods, DF≈0.826446.
Use a rate corresponding to one period; excludes cash-flow-specific timing conventions.
Explore formula and calculator →Cash runway: use available cash, net cash burn per month. Review the formula, worked example and calculation steps.
100000 cash and10000 monthly burn gives10 months.
Constant net burn; future financing, revenue changes and working capital swings are not modelled.
Explore formula and calculator →Aspect ratio: use width, height. Review the formula, worked example and calculation steps.
1920/1080 gives1.77778, equivalent to16:9.
Dimensions must use the same units.
Explore formula and calculator →Screen diagonal: use screen width, screen height. Review the formula, worked example and calculation steps.
A16 by9 inch rectangle has diagonal√337 inches.
Measures the rectangular display, excluding bezel and curved-surface effects.
Explore formula and calculator →Pixels per inch: use horizontal pixels, vertical pixels, screen diagonal. Review the formula, worked example and calculation steps.
1920×1080 on a24-inch display gives approximately91.79 PPI.
Assumes square pixels and a rectangular flat display.
Explore formula and calculator →Download time: use file size, connection speed. Review the formula, worked example and calculation steps.
1 decimal GB at100 Mbit/s takes80 seconds ideally.
Decimal network units, no protocol overhead or speed variation.
Explore formula and calculator →Split bill: use bill before tip, tip, people. Review the formula, worked example and calculation steps.
100 plus15% tip split4 ways is28.75 each.
Equal shares; any additional tax should be included in the entered bill.
Explore formula and calculator →Fuel range: use fuel available, consumption. Review the formula, worked example and calculation steps.
40L at8L/100km gives500km.
Ideal constant consumption without reserve fuel, terrain or traffic effects.
Explore formula and calculator →Travel time: use distance, average speed, break time. Review the formula, worked example and calculation steps.
150km at60km/h plus30 minutes of breaks takes3 hours.
Use realistic average speed and include expected stops.
Explore formula and calculator →Meeting cost: use participants, average hourly cost per person, duration. Review the formula, worked example and calculation steps.
6 people at30/hour for1 hour costs180.
Uses a supplied average labor cost; opportunity cost and overhead are not inferred.
Explore formula and calculator →Force: use mass, acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Net force along one axis for constant mass.
Explore formula and calculator →Acceleration: use initial velocity, final velocity, elapsed time. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Average acceleration along one axis.
Explore formula and calculator →Kinetic energy: use mass, velocity. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Classical translational energy, appropriate at speeds much smaller than light speed.
Explore formula and calculator →Gravitational potential energy: use mass, gravitational acceleration, height above reference. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Uniform gravitational field; zero height is a user-selected reference.
Explore formula and calculator →Momentum: use mass, velocity. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Classical linear momentum along the selected axis.
Explore formula and calculator →Impulse: use average force, duration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Average force in a fixed direction over the interval.
Explore formula and calculator →Work: use constant force, displacement magnitude, angle to displacement. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Constant force, straight displacement; angle is in degrees.
Explore formula and calculator →Power from work: use work, time. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Average power over the supplied interval.
Explore formula and calculator →Spring constant: use force magnitude, extension magnitude. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Linear Hooke-law region. Force and extension are magnitudes.
Explore formula and calculator →Spring energy: use spring constant, displacement. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal linear spring; displacement is relative to equilibrium.
Explore formula and calculator →Torque: use force, lever arm length, angle between arm and force. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
A scalar signed torque in the specified plane; the reference axis and force direction matter.
Explore formula and calculator →Pressure: use normal force, area. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Uniform normal force on a flat area; no gauge/absolute offset is inferred.
Explore formula and calculator →Buoyant force: use fluid density, displaced volume, gravitational acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Static fluid of uniform density; volume is displaced fluid, not necessarily the whole object.
Explore formula and calculator →Centripetal force: use mass, velocity, path radius. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Magnitude of net inward force for uniform circular motion.
Explore formula and calculator →Centripetal acceleration: use velocity, path radius. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Inward acceleration magnitude for circular motion.
Explore formula and calculator →Angular velocity: use rotation rate. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
A full turn is 2π radians; sign indicates rotation direction.
Explore formula and calculator →Point-mass moment of inertia: use mass, distance from axis. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Point-mass model. Extended shapes have different moments of inertia.
Explore formula and calculator →Rotational kinetic energy: use moment of inertia, angular velocity. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Rigid-body rotation about the axis used for the entered inertia.
Explore formula and calculator →Gravitational force: use first mass, second mass, centre-to-centre distance. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Newtonian point masses or non-overlapping spherically symmetric bodies.
Explore formula and calculator →Free-fall time: use drop height, gravitational acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Starts from rest with constant g; ignores drag.
Explore formula and calculator →Projectile range: use launch speed, launch angle above horizontal, gravitational acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Launch and landing at equal height in a uniform field; no drag.
Explore formula and calculator →Projectile maximum height: use launch speed, launch angle, gravitational acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Height above the launch point; ignores drag.
Explore formula and calculator →Projectile flight time: use launch speed, launch angle, gravitational acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Return to launch height; ignores drag and changes in g.
Explore formula and calculator →Pendulum period: use pendulum length, gravitational acceleration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Small-angle simple pendulum with negligible pivot friction.
Explore formula and calculator →Wavelength: use wave speed, frequency. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Use the wave speed in the actual medium.
Explore formula and calculator →Wave frequency: use wave speed, wavelength. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Wave speed and wavelength must describe the same medium and mode.
Explore formula and calculator →Frequency to period: use frequency. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
One full cycle per period.
Explore formula and calculator →Photon energy: use vacuum wavelength. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Vacuum wavelength; uses exact SI Planck constant and speed of light.
Explore formula and calculator →Mass–energy equivalence: use rest mass. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Rest energy only; not energy obtainable from an arbitrary process.
Explore formula and calculator →Sensible heat: use mass, specific heat capacity, temperature change. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Constant heat capacity, no phase change or losses.
Explore formula and calculator →Linear thermal expansion: use initial length, expansion coefficient, temperature change. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Linear approximation for a constant material coefficient.
Explore formula and calculator →Coulomb force: use first charge, second charge, separation. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Point charges in vacuum. Positive indicates like-charge repulsion; negative indicates attraction.
Explore formula and calculator →Capacitance: use charge magnitude, potential difference magnitude. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal linear capacitor; use charge on one plate and voltage between plates.
Explore formula and calculator →Capacitor energy: use capacitance, voltage. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal capacitor with constant capacitance.
Explore formula and calculator →Resistor power: use current, resistance. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Use DC current or AC RMS current for an ideal resistor.
Explore formula and calculator →Snell’s law: use incident refractive index, transmitted refractive index, incident angle to the normal. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Angles are measured from the surface normal. Total internal reflection has no real transmitted angle.
Explore formula and calculator →Thin lens image distance: use focal length, object distance. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Thin-lens paraxial approximation with the real-is-positive sign convention.
Explore formula and calculator →Ideal gas pressure: use amount, absolute temperature, volume. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal-gas model. Temperature is kelvin; nonideal gases may require a different equation of state.
Explore formula and calculator →Boyle’s law: use initial pressure, initial volume, final volume. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Fixed gas amount and temperature; use absolute pressures.
Explore formula and calculator →Charles’s law: use initial volume, initial temperature, final temperature. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Fixed pressure and gas amount; temperatures must be absolute.
Explore formula and calculator →Combined gas law: use initial pressure, initial volume, initial temperature. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Fixed ideal-gas amount; absolute pressures and kelvin temperatures.
Explore formula and calculator →Solution dilution: use initial concentration, stock volume, final solution volume. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Assumes conserved solute and compatible concentration/volume definitions; final volume is not solvent added.
Explore formula and calculator →Dilution factor: use final solution volume, stock aliquot volume. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
A pure volume ratio; values below1 describe concentration rather than dilution.
Explore formula and calculator →Mass to moles: use mass, molar mass. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Supply the molar mass of the actual chemical species.
Explore formula and calculator →Molar mass from mass & amount: use mass, amount. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
This calculates molar mass from measured mass and amount; it does not parse a molecular formula.
Explore formula and calculator →Particle count: use amount. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Specify what is counted: atoms, molecules, ions or formula units. Large results use floating-point display.
Explore formula and calculator →Percent yield: use actual yield, theoretical yield. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Use the same product and mass units. A result above100% can reflect impurities or measurement errors.
Explore formula and calculator →Theoretical yield from percent yield: use actual yield, percent yield. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
A supplied percentage is used; stoichiometric limiting-reagent calculation is a separate model.
Explore formula and calculator →Atom economy: use desired product molar-mass contribution, total stoichiometric reactant molar-mass contribution. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Include stoichiometric coefficients in the supplied molar-mass contributions.
Explore formula and calculator →Mole fraction: use component amount, total amount. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
All mixture components must be included in the total.
Explore formula and calculator →Mass percentage: use component mass, total solution mass. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
The denominator is total solution mass, not solvent mass.
Explore formula and calculator →Molality: use solute amount, solvent mass. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Molality is based on solvent mass; molarity is based on solution volume.
Explore formula and calculator →pH from hydrogen concentration: use hydrogen-ion concentration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal dilute-solution approximation to activity-based pH. This does not predict pH after mixing substances.
Explore formula and calculator →pOH from hydroxide concentration: use hydroxide-ion concentration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal dilute-solution approximation. The familiar pH+pOH=14 relation is temperature dependent.
Explore formula and calculator →Beer–Lambert law: use molar attenuation coefficient, optical path, concentration. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Linear absorbance model at the stated wavelength; scattering, stray light and chemical changes can invalidate it.
Explore formula and calculator →Absorbance to transmittance: use absorbance. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Assumes absorbance is defined with a base-10 logarithm.
Explore formula and calculator →Arrhenius rate constant: use pre-exponential factor, activation energy, absolute temperature. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Single Arrhenius model with constant parameters; rate-constant units depend on reaction order.
Explore formula and calculator →Gibbs free energy: use enthalpy change, temperature, entropy change. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
All quantities must refer to the same reaction, composition and conditions.
Explore formula and calculator →Boiling point elevation: use van ’t hoff factor, ebullioscopic constant, molality. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal dilute-solution colligative approximation; supply the solvent constant and effective particle factor.
Explore formula and calculator →Freezing point depression: use van ’t hoff factor, cryoscopic constant, molality. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Magnitude of the freezing-point decrease for an ideal dilute solution.
Explore formula and calculator →Osmotic pressure: use van ’t hoff factor, concentration, temperature. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal dilute solution. Concentration here is mol/m³, not mol/L.
Explore formula and calculator →Electrolysis mass: use current, time, molar mass. Review the formula, worked example and calculation steps.
Use the displayed example inputs, then follow the substituted values in the solution.
Ideal100% current efficiency; actual deposition depends on side reactions and process conditions.
Explore formula and calculator →Paint quantity: use room length, room width, wall height. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Four rectangular walls; ceilings and product-specific application losses are excluded.
Explore formula and calculator →Brick quantity: use wall area, brick face length including joint, brick face height including joint. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
One face layer, using dimensions that already include joints. Bond pattern, corners and structural requirements are not modelled.
Explore formula and calculator →Wallpaper rolls: use wall area, usable coverage per roll, waste allowance. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Supply usable roll coverage after matching the pattern. This is an area estimate, not a cutting plan.
Explore formula and calculator →Asphalt quantity: use length, width, compacted depth. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Rectangular compacted volume; density and compaction allowance must match the actual mix.
Explore formula and calculator →Board feet: use thickness, width, length. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Use actual or nominal dimensions consistently; one board foot is144 cubic inches.
Explore formula and calculator →Fence posts: use fence run, maximum post spacing. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
One open straight run. Closed loops, corners, gates and foundation design need separate planning.
Explore formula and calculator →Flooring cost: use floor area, material price per area, waste allowance. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Material-only estimate; pack sizes, installation and tax are excluded.
Explore formula and calculator →Stair stringer length: use total rise, total horizontal run. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Geometric diagonal only, excluding end details. This does not verify a compliant stair design.
Explore formula and calculator →Ramp slope: use vertical rise, horizontal run. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Horizontal run is not sloping length. This reports geometry, not accessibility or building-code compliance.
Explore formula and calculator →Roof pitch angle: use rise, horizontal run. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Same length units for rise and horizontal run.
Explore formula and calculator →Drywall sheets: use area to cover, usable area per sheet, waste allowance. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Area estimate; layout, openings, sheet orientation and fire/moisture specifications are not selected.
Explore formula and calculator →Concrete bags: use required concrete volume, mixed yield per bag. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Supply the manufacturer’s mixed yield. Mix strength, reinforcement and structural design are not inferred.
Explore formula and calculator →Post-hole concrete: use hole diameter, hole depth, number of holes. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Ideal cylindrical holes and round posts; excludes waste and irregular excavation.
Explore formula and calculator →Rebar mass: use bar diameter, total bar length, material density. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Smooth-cylinder geometric estimate; nominal bar dimensions and actual manufacturing tolerances may differ.
Explore formula and calculator →Rectangular pool volume: use length, width, average filled depth. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Rectangular footprint and supplied average water depth; steps and irregular contours are excluded.
Explore formula and calculator →Recipe scaling: use original ingredient amount, original servings, desired servings. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Linear ingredient scaling; cooking time and vessel geometry may need separate adjustment.
Explore formula and calculator →Grams to cups: use ingredient mass, supplied bulk density, cup volume. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Density depends on ingredient and packing. Supply a measured density and the cup standard you use.
Explore formula and calculator →Millilitres to grams: use volume, density. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Density is ingredient- and temperature-dependent; mL and grams are not generally interchangeable.
Explore formula and calculator →Coffee to water ratio: use water mass, water to coffee ratio. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
The ratio is supplied by you; beverage yield differs from input water because grounds retain liquid.
Explore formula and calculator →Baker’s percentage: use ingredient mass, total flour mass. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Flour is100%; ingredient percentages can exceed100 and do not have to sum to100.
Explore formula and calculator →Dough hydration: use total water mass, total flour mass. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Include water and flour from preferments consistently. This is not a fermentation-time prediction.
Explore formula and calculator →Brine salt mass: use water mass, target salt by total solution mass. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Weight/weight salt percentage in the total solution. This is ingredient arithmetic, not food-preservation safety guidance.
Explore formula and calculator →Pizza size comparison: use first pizza diameter, number of first pizzas, comparison pizza diameter. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Compares circular surface areas, ignoring crust width, thickness and toppings.
Explore formula and calculator →Round cake pan scaling: use original pan diameter, new pan diameter, original batter depth. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Cylindrical pan volumes; does not predict baking time or doneness.
Explore formula and calculator →ABV from specific gravity: use original specific gravity, final specific gravity. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Approximate brewing gravity model; not an analysis of a finished beverage or blood alcohol.
Explore formula and calculator →Alcohol dilution: use starting solution volume, starting abv, target abv. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Ideal additive-volume approximation; mixing contraction and temperature effects are excluded.
Explore formula and calculator →Exponential population growth: use initial population, continuous growth rate, elapsed time. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Continuous deterministic model, not a prediction of actual births, deaths or resources.
Explore formula and calculator →Logistic population growth: use initial population, carrying capacity, growth rate. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Fixed carrying capacity and growth rate, with initial population at or below capacity.
Explore formula and calculator →Cell doubling time: use initial count, final count, elapsed time. Review the formula, worked example and calculation steps.
Use the example inputs to explore this model; the solution shows each supplied quantity.
Assumes exponential growth between two measurements; does not validate a culture model.
Explore formula and calculator →Allele frequency: use aa count, aa count, aa count. Review the formula, worked example and calculation steps.
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Diploid, biallelic count arithmetic. No inference about ancestry, diagnosis or individual traits.
Explore formula and calculator →Hardy–Weinberg proportions: use frequency of allele a. Review the formula, worked example and calculation steps.
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Ideal random-mating biallelic population model; real populations may violate its assumptions.
Explore formula and calculator →Mortality proportion: use deaths in the defined cohort, initial cohort size. Review the formula, worked example and calculation steps.
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A cohort proportion over a supplied period, not a person-time rate or survival analysis.
Explore formula and calculator →Seed germination rate: use seeds germinated, seeds tested. Review the formula, worked example and calculation steps.
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A count from a defined test; future field germination can differ.
Explore formula and calculator →Plant spacing estimate: use planting area, row spacing, within-row spacing. Review the formula, worked example and calculation steps.
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Area-density estimate only; paths, borders and actual row layout are excluded.
Explore formula and calculator →Seed quantity: use sowing area, supplied seed rate. Review the formula, worked example and calculation steps.
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Supply a crop- and site-appropriate rate; germination adjustment is not inferred.
Explore formula and calculator →Tree basal area: use stem diameter at the measurement height. Review the formula, worked example and calculation steps.
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Circular stem cross-section; diameter must be measured at a consistent height.
Explore formula and calculator →Daily light integral: use constant ppfd, photoperiod. Review the formula, worked example and calculation steps.
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Assumes constant photon flux during the light period; variable outdoor light requires integration.
Explore formula and calculator →DNA copy number: use dna mass, sequence length, molar mass per base pair. Review the formula, worked example and calculation steps.
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Default660 g/(mol·bp) is an approximate double-stranded DNA model; supply the appropriate molecular mass.
Explore formula and calculator →DNA to mRNA: use dna sequence · a c g t or n, input strand. Review the formula, worked example and calculation steps.
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Canonical DNA transcription notation only; no gene prediction, splicing or clinical interpretation.
Explore formula and calculator →Solar panel energy: use array rated power, peak sun hours per day, system performance ratio. Review the formula, worked example and calculation steps.
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Supplied peak sun hours and performance ratio; no location-specific irradiation or financial return is inferred.
Explore formula and calculator →Required solar capacity: use daily energy target, peak sun hours, performance ratio. Review the formula, worked example and calculation steps.
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Steady daily-energy estimate; storage, seasonal variation and grid constraints require separate design.
Explore formula and calculator →Hydroelectric power: use flow rate, net head, efficiency. Review the formula, worked example and calculation steps.
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Uses supplied net head and efficiency; ignores changes in flow and detailed hydraulic design.
Explore formula and calculator →Wind power: use rotor diameter, wind speed, air density. Review the formula, worked example and calculation steps.
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Ideal swept-area power model; coefficient is capped at the Betz limit. Actual turbines have cut-in, cut-out and rated-power limits.
Explore formula and calculator →Daily water demand: use people, supplied demand per person. Review the formula, worked example and calculation steps.
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A supplied usage scenario; no regional entitlement or minimum supply standard is inferred.
Explore formula and calculator →Dripping faucet water loss: use drops per minute, average drop volume. Review the formula, worked example and calculation steps.
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Drop volume varies; use a measured value where possible.
Explore formula and calculator →Emissions from activity: use activity quantity, supplied emissions factor. Review the formula, worked example and calculation steps.
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Use a factor appropriate to the geography, year, lifecycle boundary and activity units. No live emissions factors are embedded.
Explore formula and calculator →Shannon diversity index: use species counts, logarithm base. Review the formula, worked example and calculation steps.
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Probabilities are estimated from counts; zero-count categories contribute zero.
Explore formula and calculator →Simpson diversity · 1−Σp²: use species counts. Review the formula, worked example and calculation steps.
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Uses1−Σp², not the reciprocal or finite-sample unbiased variant.
Explore formula and calculator →Race time from pace: use race distance, average pace. Review the formula, worked example and calculation steps.
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Assumes a constant average pace; course and conditions are not modelled.
Explore formula and calculator →Swimming pace: use elapsed time, distance. Review the formula, worked example and calculation steps.
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Elapsed average, including any rests that you include in the supplied time.
Explore formula and calculator →Bike cadence & speed: use wheel circumference, pedal cadence, front chainring teeth. Review the formula, worked example and calculation steps.
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Ideal gear relationship without wheel slip; wheel circumference should reflect the actual tire.
Explore formula and calculator →Batting average: use hits, at bats. Review the formula, worked example and calculation steps.
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Baseball batting average; walks and sacrifice events do not automatically count as at bats.
Explore formula and calculator →Cricket batting strike rate: use runs, balls faced. Review the formula, worked example and calculation steps.
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Supply counted deliveries under the match’s scoring rules.
Explore formula and calculator →Cricket bowling average: use runs conceded, wickets credited. Review the formula, worked example and calculation steps.
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Use runs and wickets credited to the bowler, excluding unrelated extras where the rules require.
Explore formula and calculator →Winning percentage: use wins, losses, ties. Review the formula, worked example and calculation steps.
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Ties count as half a win in this convention; some competitions use another rule.
Explore formula and calculator →Elo rating update: use your rating, opponent rating, actual score. Review the formula, worked example and calculation steps.
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Single-game classic logistic Elo with supplied K; federation-specific adjustments are excluded.
Explore formula and calculator →One-rep max · Epley estimate: use lifted load, completed repetitions. Review the formula, worked example and calculation steps.
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Epley estimate for2–10 repetitions; one completed rep returns its actual load. An estimate does not establish a safe training load.
Explore formula and calculator →E-bike range: use usable battery energy, average consumption. Review the formula, worked example and calculation steps.
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Supply measured consumption and usable capacity. Terrain, wind, assistance setting and temperature affect actual range.
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