What if I don’t know the population size?

Leave it empty. For large populations (over roughly 20,000 people) the result barely changes, so it is calculated as if the population were infinite.

Which confidence level should I use?

95% is the most common in research and theses. 90% needs fewer responses and 99% needs quite a few more.

How many responses do I need for a thesis?

It depends on your population and the margin your supervisor asks for. With a population of 500, 95% confidence and ±5%, you need 218 responses.

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Sample size calculator

Enter your population size, confidence level and the margin of error you can accept. It tells you how many responses you need and, if you know your usual response rate, how many people to invite.

Population size (optional)

Leave empty if it is very large or unknown

Confidence level

Margin of error

Expected response rate (%) (optional)

To know how many people to invite

Responses needed

385

The calculation runs in your browser. We don’t store what you type.

How it’s calculated

It uses the formula for estimating a proportion: n₀ = Z² × p × (1 − p) / e², where Z comes from the confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), e is the margin of error and p is the expected proportion.

Since p is rarely known in advance, 0.5 is used. It is the case that needs the most responses, so the result works for every question in the survey.

If you know the population (N), the finite population correction is applied: n = n₀ / (1 + (n₀ − 1) / N). That is why small populations need fewer responses.

How to read the result

With 95% confidence and a ±5% margin, if 60% answer “yes”, the true value in the population is between 55% and 65% in 95 out of 100 samples.
Going from ±5% to ±3% almost triples the responses you need. Pick the margin your decision needs, not the smallest one possible.
The math assumes a random sample. If only people who want to answer do, more responses won’t fix that bias.

Frequently asked questions

What if I don’t know the population size?: Leave it empty. For large populations (over roughly 20,000 people) the result barely changes, so it is calculated as if the population were infinite.
Which confidence level should I use?: 95% is the most common in research and theses. 90% needs fewer responses and 99% needs quite a few more.
How many responses do I need for a thesis?: It depends on your population and the margin your supervisor asks for. With a population of 500, 95% confidence and ±5%, you need 218 responses.

Is it for your thesis?See the step-by-step guide to running your thesis survey: sample, questionnaire, consent, pilot test and analysis.Thesis surveys

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