Survey Sample Size Calculator

What this generator does

Computes the sample size needed to estimate a proportion within a stated margin of error, then applies Cochran's finite population correction when the group is a known size. It also runs the arithmetic backwards: the recommended figure is fed through the margin-of-error formula to confirm it genuinely delivers the precision asked for, rather than trusting the derivation.

How to use this tool

1. Set the margin of error you want, in percentage points.
2. Choose a confidence level — 95% is the convention.
3. If you are surveying a known, limited group, tick the box and give its size.
4. The required sample updates as you type.

Understanding the controls

Margin of error

How far out the answer is allowed to be, in percentage points, either side. The relationship is quadratic: halving the margin needs roughly four times the responses, which is the single most useful thing to know before commissioning a survey.

Confidence level

How often the interval would contain the true value across many repeats. 95% is the convention. Going to 99% costs about 70% more responses, which is rarely worth it for an internal decision.

Expected proportion

Your estimate of the answer. 50% needs the largest sample, which is why it is the default — it is the safe choice when you do not know. Setting it to 10% cuts the requirement substantially, but only helps if the real answer is anywhere near it.

The population is limited

Tick this when you are sampling a group of known size. The correction is significant whenever your sample would be a meaningful fraction of the whole, and it is the part most calculators skip.

Common use cases

• Working out how many responses a survey needs before running it
• Checking whether a survey that has already closed had enough responses to say anything
• Sizing a sample of a known population — a company, a school, a membership list
• Showing a stakeholder why halving the margin of error costs four times the responses
• Deciding whether a smaller, cheaper sample is good enough for the decision at hand

How this generator works

The base figure comes from the standard formula for estimating a proportion: z squared times p times one minus p, divided by the margin squared, where z is the two-sided critical value for the confidence level. When a population size is given, Cochran's correction divides that by one plus the excess over the population, and the result is capped at the population itself. The answer is then verified by recomputing the margin of error that the recommended sample delivers and comparing it to the request.

Randomness and fairness

Nothing here is random. The same inputs give the same answer every time, which is what a calculator should do.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

• Simple random sampling from the population.
• You are estimating a single proportion rather than comparing groups.
• The normal approximation is adequate, which it is at these sample sizes.

Limitations and good to know

• This sizes an estimate of a proportion. Sizing for a difference between two groups, or for a mean rather than a proportion, uses different formulas.
• It assumes simple random sampling. Cluster and stratified designs need a design effect applied on top, often between 1.5 and 2.
• It says nothing about response rate. If a third of people reply, you need to invite three times this many.
• Non-response bias is not a sample size problem and cannot be fixed by asking more people.

Common mistakes

Ignoring the population size for a small group

For a 500-person company the requirement drops from 384 to 218. Sampling a meaningful fraction of a population genuinely needs fewer people.

Confusing invitations with responses

This number is completed responses. At a 30% response rate you need to invite more than three times as many.

Setting the expected proportion optimistically

Moving it away from 50% lowers the requirement, but if the true answer turns out to be near 50% your margin will be wider than you planned. 50% is the conservative choice for a reason.

Practical tips

• Try five points and three points side by side. The jump from 385 to 1,068 usually settles the argument about precision faster than any explanation.
• For an internal survey of a known team, always tick the population box — the saving is often more than half.
• Decide the margin from the decision you are making. If you will act the same way at 40% and 45%, you do not need five-point precision.

Privacy and your data

Everything is calculated in your browser. No figures you enter are transmitted or stored between visits.

Frequently asked questions

Why do I sometimes see 384 and sometimes 385?

Because of the critical value used. With z as 1.96 the answer rounds to 385; with the more precise 1.959964 it rounds to 384. The difference is immaterial to any real survey.

Does a bigger population need a bigger sample?

Barely. Above about 20,000 the required sample stops moving. That is why national polls and city polls use similar numbers, which surprises people.

How is this different from the A/B test calculator?

That one sizes a test for detecting a difference between two variants. This one sizes an estimate of a single proportion, which is the survey question rather than the experiment question.