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

Formula

n = z² × p(1−p) / e²

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

  1. Enter the confidence level (e.g. 95%) — this determines the z-score used in the formula.
  2. Enter the margin of error as a percentage (e.g. 5% means ±0.05).
  3. Enter the expected proportion if known; use 50% when unknown — it gives the largest (most conservative) sample size.
  4. Optionally enter the population size to apply the finite population correction (FPC).
  5. The calculator applies n = z² × p(1−p) / e², then rounds up to the nearest whole number.
  6. 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.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu