What is margin of error?

Margin of error (MoE) expresses the maximum expected difference between the true population value and a sample estimate. A ±5% MoE at 95% confidence means that if you ran the same survey 100 times, 95 of those results would fall within 5 percentage points of the true answer.

What confidence level should I use?

95% is the academic and industry standard for most surveys and studies. Use 99% when the cost of being wrong is high (medical, legal). Use 90% when resources are limited and a slightly wider error range is acceptable.

Why does changing population size barely affect the result for large populations?

Once a population exceeds roughly 20,000, the finite population correction factor approaches 1 and has negligible effect. Sample size is driven primarily by the desired precision (margin of error), not the population size.

What is the response proportion (p)?

It is the estimated share of respondents expected to choose a given answer. When unknown, use 50% (0.5) — this produces the largest (most conservative) sample size. If you know from prior data that roughly 20% will say yes, enter 20% to get a smaller required sample.

Does the calculator assume simple random sampling?

Yes. The formula assumes a simple random sample. If you use stratified, cluster, or other complex sampling methods, the required sample may differ. Consult a statistician for complex designs.

Why is the result rounded up?

Sample size must be a whole number. Rounding down would give a sample slightly below the precision target, so we always round up to guarantee the stated margin of error is met.

Is the sample size the number of people to invite?

No. It is the number of completed responses. Divide it by your expected response rate: if 20% of people answer, invite 385 ÷ 0.20 = 1,925 people for 385 responses.

Why do some calculators show 384 instead of 385?

The unrounded value for an infinite population is 384.16. This calculator always rounds up so the margin of error is met, which gives 385. Calculators that round to the nearest whole number show 384.

Sample Size Calculator

Enter your population size, confidence level, and margin of error to instantly calculate the minimum sample size needed for a statistically valid survey.

For a large population at 95% confidence and a ±5% margin of error, you need 385 completed responses.

Study Parameters

Population Size

Total number of people in the group you are studying. Use 1,000,000 if unknown or very large.

Confidence Level

How certain you need to be that your results reflect the true population value.

Margin of Error (%)

Acceptable range of error. Smaller values require larger samples.

Response Proportion (%)

Expected share answering "yes". Use 50% for the most conservative (largest) sample.

Required Sample Size

—

responses needed

Quick Presets

Quick answer

For a large population at 95% confidence and a ±5% margin of error, you need 385 completed responses. Smaller populations need fewer once the finite population correction is applied, and a tighter margin needs far more: ±3% takes 1,066.

Examples

Population	95%, ±5%	95%, ±3%
500	218	341
1,000	278	517
5,000	357	880
10,000	370	965
1,000,000	385	1,066

Enter your population and margin.

Summary

This sample size calculator uses the standard statistical formula to determine how many responses you need to achieve a given margin of error and confidence level. It accounts for finite population correction when your population is known and small relative to the sample. Results are rounded up to the nearest whole number so your study always meets the stated precision.

How it works

Enter your total population size (or leave at 1,000,000 for large or unknown populations).
Select a confidence level — 95% is the most common choice for surveys.
Set your desired margin of error (e.g., ±5% means results are accurate within 5 percentage points).
Optionally adjust the expected response proportion (default 50% gives the most conservative, largest sample).
The calculator applies the standard formula and finite population correction, then rounds up to give the minimum required sample size.

Use cases

Plan the number of survey responses needed before launching a customer satisfaction study.
Determine how many product testers are required for statistically meaningful A/B test results.
Size a market research project to justify a budget request.
Validate that an existing dataset is large enough to draw reliable conclusions.
Academic researchers planning experiments requiring a specific confidence level.
Political polling — estimate how many voters to interview for a ±3% margin of error.
Quality control teams calculating inspection sample sizes from production batches.
Healthcare studies sizing patient cohorts for clinical significance.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu