Math & Statistics

Sample Size Calculator

Works out how many records you need to sample for a stated confidence and margin of error.

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How to use this tool

  1. Paste one or more population sizes, one per line.
  2. Set the confidence level and the margin of error you are willing to live with.
  3. Leave the expected proportion at 50% unless you have a prior estimate — 50% gives the largest, safest sample.
  4. Select Calculate, then divide by your expected response rate to get the number of invitations to send.

What sample size calculator does

The count you need depends far more on the precision you want than on how big the population is. Going from a ±5% margin to ±2% multiplies the sample by roughly six; going from a population of fifty thousand to five million barely moves it at all. Paste several population sizes at once and that relationship becomes obvious in a way a single answer never makes it.

The finite population correction is applied, so a small population gets a correspondingly smaller sample rather than the textbook figure for an unlimited one. The share of the population each sample represents is shown too. This is the number of usable responses or records you need — not the number of invitations to send, which is this figure divided by the response rate you expect.

Frequently asked questions

Because precision depends on how many observations you have, not on what fraction of the population they are. Beyond roughly twenty thousand the correction is negligible — which is why a national poll and a city poll need about the same number of responses.

Leave it at 50% unless you have a real prior estimate. Fifty per cent maximises the variance and therefore the required sample, so it is the safe assumption. If you know the answer is nearer 10% you can enter that and get a smaller sample, at the cost of being wrong if the estimate was off.

No — it is the number of usable responses or records you need. Divide by the response rate you actually expect to get the number of invitations. Treating the two as the same is the reason surveys close under-powered.

For estimating a rate — what share of records carry a defect — yes, and the finite population correction matters more there because populations are often small. It is not the right tool for acceptance sampling against a zero-defect standard, which uses a different model.