FreeToolStation

Sample Size Calculator

How many responses a survey needs to be worth reporting.

Statistics Calculators Free, no sign-up Runs in your browser

Use 50 if you do not know: it gives the largest, safest sample.

Optional. Reduces the sample needed for a small population.

The number to invite is the sample divided by this.

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Responses needed
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People to invite
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With a finite population
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Critical value
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Margin this achieves
Margin of errorResponses neededWith your population

About the Sample Size Calculator

Sample Size Calculator answers the question that should come before a survey is sent: how many responses are needed for the result to be worth reporting? It inverts the margin of error formula, so you choose the precision you want and it returns the sample that delivers it.

The arithmetic is unforgiving because the margin falls with the square root of the sample. A five per cent margin needs about 385 responses; three per cent needs 1,068; one per cent needs over 9,600. Each step in precision costs several times the previous one, which is why almost every published survey settles around a thousand.

The population correction and the response rate are where theory meets practice. For a small population -- a company, a school, a membership -- the required sample drops substantially, because sampling a large share of a small group is more informative. And since not everyone replies, the invitation list has to be the sample divided by the expected response rate, which is the number you actually need to send.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

Looking for something this does not cover? FreeToolsZone.org is more free browser-based tools, organised by job, and it is worth a look if sample size calculator is only part of what you are working on.

How to use the Sample Size Calculator

  1. Choose confidence levelThe fields below change to match what you pick, so only the figures that matter to your case are asked for.
  2. Enter margin of error wanted (%), expected result (%) and population sizeDecimals are fine, and thousands separators are accepted and ignored.
  3. Read the responses needed, people to invite and with a finite populationThe figures update as you type. The Calculate button is there if you would rather press something, but nothing waits for it.
  4. Copy or check the resultCopy the summary with the copy button, or open the table to check it row by row.

Features

  • Shows responses needed, people to invite, with a finite population, critical value and margin this achieves together, so you are not running it twice
  • A results table you can read across
  • Updates as you type, with no button to press and no page reload
  • Copy the result in one click
  • Free, no sign-up, and it runs entirely in your browser

Who uses this tool

The sample size calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

  • Sizing a customer survey before sending it
  • Working out how many people to invite at a known response rate
  • Costing the precision of a market research project
  • Checking whether a completed survey had enough responses

Frequently asked questions

What expected result should I use?

Fifty per cent if you do not know, because it requires the largest sample and therefore cannot leave you short. If you expect a lopsided result, using it reduces the sample needed.

Why does a smaller population need fewer responses?

Because you are sampling a larger share of it. Surveying 300 of 1,000 members tells you far more than 300 of ten million.

Does the sample need to be random?

Yes, or the margin of error means nothing. A self-selected sample of any size can be badly biased, and no sample-size calculation fixes that.

If the sample size calculator is not quite what you need, these other free tools solve closely related problems, and there are 13 more in statistics calculators.

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Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.