Pick a survey sample size

How many people to ask before the answer means anything: Cochran's formula turns confidence and margin into a headcount.

Tools used in this guide

The job

"95% confident, ±5%" is the standard survey promise — and it implies a specific n. Cochran's formula n₀ = z²·p(1−p)/e² is the usual first answer.

Compute n

Choose a confidence level (90/95/99%), enter the margin of error you can live with, and the expected proportion (leave 0.5 when unknown — it is the conservative maximum). A population size applies finite-population correction.

95% and ±5% at p=0.5 is the famous n≈385 — enough for any large population.
Small populations shrink n fast: at N=1000 the same spec needs ≈278.

Worked example

A product team wants ±3% at 95% on a 50,000-user base: n₀ = 1068. Expected proportion stays 0.5 because they do not know it — guessing lower would shrink n dishonestly.

Where it stops

Proportions only — not means, not cluster or stratified designs, and no nonresponse padding (budget extra invites yourself). The formula assumes simple random sampling.