Sample Size for Proportion
Find the minimum sample size needed to estimate a population proportion at your chosen confidence level and margin of error.
Parameters
How confident you need to be that the true value lies within the margin.
Acceptable ±error around the estimated proportion (e.g. 5 means ±5 percentage points).
Best estimate of the true proportion. Use 50% if unknown — it gives the most conservative result.
Enter if sampling from a finite population to apply the finite population correction.
Required Sample Size
Enter parameters and click Calculate
Calculation Breakdown
Formula
Where z = z-score for the confidence level, p = expected proportion, e = margin of error (as a decimal). With a finite population N: nc = n / (1 + (n−1) / N).
Summary
Find the minimum sample size needed to estimate a population proportion at your chosen confidence level and margin of error.
How it works
- Enter the confidence level (e.g. 95%) — this determines the z-score used in the formula.
- Enter the margin of error as a percentage (e.g. 5% means ±0.05).
- Enter the expected proportion if known; use 50% when unknown — it gives the largest (most conservative) sample size.
- Optionally enter the population size to apply the finite population correction (FPC).
- The calculator applies n = z² × p(1−p) / e², then rounds up to the nearest whole number.
- If a finite population N is given, the corrected size is n_c = n / (1 + (n−1)/N).
Use cases
- Plan a survey to estimate what fraction of customers prefer a product feature.
- Design a clinical study to estimate a disease prevalence rate.
- Determine how many voters to poll to estimate election-support percentages.
- Set sample size for quality-control inspection of a production batch.
- Calculate how many website visitors to include in an A/B test proportion analysis.
- Size a market-research study when the true proportion is unknown.