About this tool
The Sample Size Calculator is a free, in-browser tool that computes how many responses a survey or study needs to estimate a proportion at your chosen confidence level and margin of error. It uses Cochran's formula n₀ = z²·p(1−p)/e² and, when you provide a population size, applies the finite-population correction n = n₀ / (1 + (n₀ − 1)/N).
Enter the confidence level, the acceptable margin of error, the expected proportion (use 50% if unsure — it is the most conservative) and optionally the population size. The required sample size, the infinite-population size and the z value used are shown instantly, all computed locally in your browser.
Frequently asked questions
Why use 50% as the expected proportion?
p(1−p) is largest at p = 50%, so it yields the largest — safest — sample size. If prior data suggests the true proportion is nearer 10% or 90%, entering it will shrink the required sample.
What do the classic numbers 385 and 278 come from?
At 95% confidence, 5% margin and p = 50%, Cochran's formula gives 384.16, rounded up to 385 for an unlimited population; with a population of 1,000 the finite-population correction reduces it to 278.
When does the population size matter?
Only when the sample would be a noticeable fraction of the population (roughly above 5%). For large populations the correction is negligible, which is why the field is optional and blank means unlimited.
Does this account for non-response?
No — the result is the number of completed responses you need. Divide by your expected response rate to get the number of invitations (e.g. 385 needed ÷ 0.20 response rate ≈ 1,925 invitations).