Sample Size Calculator
Work out how many people to survey for a target margin of error and confidence level, with an optional finite-population correction.
How it works
n₀ = z² × p(1 − p) ÷ E², then n = n₀ × N ÷ (n₀ + N − 1) for a finite population N
The base sample size n₀ depends on three things: the z-value for your confidence level, the margin of error E you can tolerate (as a decimal), and the expected proportion p. Uncertainty peaks at p = 0.5, so using 0.5 gives the largest, safest sample when you have no prior estimate. If the whole population is small, the finite-population correction pulls the number down, because a sample is a bigger slice of a small group.
Worked example
For a 95% confidence level, a 5% margin of error and p = 0.5, n₀ = 1.96² × 0.25 ÷ 0.05² = 384.16, so you need 385 responses. Cap the population at 10,000 and the finite correction lowers that to about 370.
Frequently asked questions
Why is 0.5 the default proportion?
The product p(1 − p) is largest at p = 0.5, which maximizes the required sample. Using it guarantees you have enough respondents no matter how the results turn out, which is why pollsters default to it.
When does population size actually matter?
Only when your sample is a meaningful fraction of the whole group. Sampling 400 from a town of 2,000 benefits from the correction; sampling 400 from a country of millions does not — the infinite-population figure is fine.
Does this account for non-response?
No. It gives the number of completed responses you need. If you expect a 40% response rate, divide by 0.4 to find how many people to invite so enough actually reply.
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For education — check assumptions (sample size, distribution) before using statistics in real decisions.