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Sample size calculator

Find the survey sample size needed for a population, confidence level and margin of error.

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Enter Population size, Confidence level, Margin of error (%) and the Sample size calculator works out Required sample size straight away. For instance, with Population size = 10,000, Confidence level = 90% and Margin of error (%) = 5 it returns Required sample size = 264.

How to use it

  1. Enter your values: Population size, Confidence level, Margin of error (%).
  2. Read the result instantly: Required sample size.

Frequently asked questions

What does the Sample size calculator actually compute?

It takes Population size, Confidence level and Margin of error (%) and derives Required sample size from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

3 values: Population size, Confidence level and Margin of error (%). Nothing else is required — no account, no file upload.

Can you show a worked example?

With Population size = 10,000, Confidence level = 90% and Margin of error (%) = 5, the calculator returns Required sample size = 264. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Population size = 20,000, Confidence level = 95% and Margin of error (%) = 5.5 instead, Required sample size goes from 264 to 313 — which is why it is worth testing a few scenarios rather than trusting a single figure.

Which “Confidence level” option should I choose?

You can pick between « 90% », « 95% » and « 99% ». Each one changes what the calculator works out, so switch and compare — the default is « 90% ».

What does it give for smaller values?

Scaled down to Population size = 5,000, Confidence level = 90% and Margin of error (%) = 4.5, Required sample size comes out at 314. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

What is the difference between the Sample size calculator and the Sample Mean Calculator?

This one returns Required sample size; the Sample Mean Calculator returns Result. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Sample Standard Deviation Calculator is the closest one after this: Compute the sample standard deviation (n−1), variance, mean and detect outliers.

Further reading

All guides →
ExplainerA Country of 68 Million Needs Fifteen More People Than a Town of 10,000The population barely enters the sample size formula. What does enter it is the margin of error, and halving that margin quadruples the survey — from 385 people to 1,537.ExplainerQuadruple the Sample to Halve the IntervalA mean of 100 with a standard deviation of 15 over 30 observations gives 100 ± 5.37 at 95 %. Going to 120 observations gives ± 2.68 — exactly half, because the sample size enters under a square root.ExplainerSixty Per Cent Over Fifty Games Means Anything From 46 to 7430 wins in 50 games is a win rate of 60 %. The 95 % interval around it runs from 46.4 % to 73.6 % — twenty-seven points wide, and wide enough to contain a losing record.ExplainerAn Error Bar That Shrinks Is Not the Standard DeviationFor 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.ExplainerIf the Variance Is Not the Mean, It Is Not PoissonWith an average of five events per interval, exactly three occur 14.0 % of the time, none at all 0.7 %, and ten or more 3.2 % — about once every 31 intervals. The distribution has one parameter, and it sets both the mean and the variance.ExplainerAn r of 0.85 That Proves NothingFive points give r = 0.853, which sounds strong. The threshold for significance at five points is 0.878, so this one falls short — and a perfect parabola scores exactly zero.