Finite Population Sample Size Calculator

Statistical sample size

Three things drive the statistical sample size: the margin of error E you can live with, the confidence level you pick (1.96 for 95%, 2.576 for 99%), and the population N when it happens to be finite. Cochran laid out the classic version back in 1977 as n₀ = z² · p · (1−p) / E², with a finite-population correction on top: n = n₀ / (1 + (n₀ − 1)/N). For a quantitative variable whose variance σ² you don't know, you fall back on n = (z·σ/E)². Plug in N = 10,000, 95% confidence, E = 5% and p = 0.5 and you land near n ≈ 370.

Applications

It shows up in opinion polling (Datafolha, IBOPE), in the big social and economic surveys (IBGE PNAD, POF), in industrial sampling that follows the ABNT NBR 5426 standards, and in academic work headed for an ethics committee or a clinical trial plan.

FAQ

Why does the sample size plateau for large N? Cochran's correction converges, so past roughly 100,000 the required n hardly budges. A 1,067-respondent sample at 95% CI and E = 3% already covers populations in the millions.

What if I don't know σ? Run a small pilot study, borrow a figure from the literature, or for normally distributed data lean on the range/4 or range/6 rule.

Stratified or simple random sampling? When each stratum is fairly homogeneous inside, stratified sampling cuts the variance for the same n. Just remember to split n across the strata proportionally, or by Neyman allocation.