Sample Size Calculator

For a proportion, n₀ = z² p(1 − p) / E²: z is the normal quantile for the confidence level (1.96 at 95 %), p the proportion you expect and E the half-width you can accept. For a mean the variance p(1 − p) is replaced by σ². The result is rounded up. If the population is finite, Cochran's correction n = n₀ / (1 + (n₀ − 1)/N) reduces it — noticeably only when n₀ is a sizeable fraction of N. The table repeats the calculation at 90, 95 and 99 % so the cost of extra confidence is visible.

p = 50 % maximises p(1 − p) and so gives the largest, safest n; a smaller or larger expectation shrinks n but widens the real margin if it turns out wrong, which is why the page flags it. σ for a mean cannot be calculated here — it comes from a pilot, an earlier study or the literature. The confidence level is a convention, not a law; 95 % is common, nothing more. Enter a sample size you already have and the page reports the margin it achieves, with the finite-population factor when N is given.

This is the simple random sampling formula. Stratified or cluster designs, non-response, design effects and power for detecting a difference between two groups are not modelled — for the last, the A/B Test page computes sample size for two proportions. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.