Why use 50% when the proportion is unknown?

The product p(1−p) is maximized at p = 0.5, which yields the largest — and most conservative — sample size. Using 50% ensures your study is adequately powered regardless of the actual proportion.

What is the finite population correction (FPC)?

When your population is small relative to the sample, the standard formula over-estimates the required size. The FPC formula n_c = n / (1 + (n−1)/N) reduces it. The correction matters most when n/N exceeds 5%.

Which z-scores correspond to common confidence levels?

90% → 1.645, 95% → 1.960, 99% → 2.576, 99.9% → 3.291. The calculator uses these exact values.

Does the formula assume a simple random sample?

Yes. The formula is derived for simple random sampling (SRS). Cluster or stratified designs require design-effect adjustments beyond this calculator.

Why is the result always rounded up?

The formula produces a real number. You must collect whole observations, so you always round up (ceiling) to guarantee the margin of error does not exceed your target.

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

Confidence Level

How confident you need to be that the true value lies within the margin.

Margin of Error (%)

Acceptable ±error around the estimated proportion (e.g. 5 means ±5 percentage points).

Expected Proportion (%)

Best estimate of the true proportion. Use 50% if unknown — it gives the most conservative result.

Population Size (optional)

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: n_c = 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.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu