Sample size calculator

Sample size calculator: what it is for

Choose the confidence level (90%, 95%, 98% or 99%), the margin of error, the expected proportion and, if you want, the population size. The calculator uses the proportion formula with finite population correction and shows how many responses you need. In reverse mode, enter how many responses you have and see the margin of error. A table compares margins from 1% to 10% at the three most used confidence levels.

The calculations run in your browser; nothing you type is sent to servers.

How to use

1. Choose the confidence level and margin of error.
2. Enter the population, if it's small.
3. See how many responses you need.

When to use it

• Plan market research and satisfaction surveys.
• Size questionnaires for a thesis.
• Check the margin of error of a poll.

Frequently asked questions

Which formula is used?

For proportions, n0 = z² · p · (1 − p) / e², where z comes from the confidence level (1.96 for 95%), p is the expected proportion and e is the margin of error. For a finite population, the correction n = n0 / (1 + (n0 − 1) / N) is applied.

Why use 50% as the expected proportion?

It is the value that gives the largest possible sample, so it's the safest when you have no idea of the result. With 95% confidence and a 5% margin of error, it leads to the famous 385 responses for a large population.

Does population size matter much?

Only when it's small. For populations above a few tens of thousands, the sample needed barely changes. A city of 100,000 and a country of 300 million need practically the same number of responses for the same margin of error.

Is it really free?

Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.

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