Sample size · population proportion
Sample size · population proportion: use confidence level, margin of error, expected population proportion. Review the formula, worked example and calculation steps.
Inputs
Use the units shownEnter your values and select Calculate.
Formula & explanation
Variables & units
- Confidence level
- Select an option
- Margin of error
- percentage points · minimum 0.01, maximum 99
- Expected population proportion
- probability · minimum 0.000001, maximum 0.999999
- Population size · 0 means large/unknown
- Numeric value · minimum 0, maximum 1000000000
Worked example
95% confidence, 5 percentage points margin and p=0.5 needs 385 observations for a large population.
Assumptions
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.
Formula version 1.0.0. JavaScript floating-point arithmetic applies. Results display up to 6 decimal places; stored values retain available precision. Use the units shown.
Practice with an example
Use the default input values to find the answer. The reset icon restores those values.
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