Sample Size Calculator

In short Sample size is the margin-of-error formula solved for n: n = z²·p(1−p) ÷ E². At 95% confidence with an assumed 50/50 split, ±5 points needs 385 responses, ±3 points needs 1,068, ±2 points needs 2,401 and ±1 point needs 9,604. Those four numbers show the whole shape of the problem — every halving of the margin costs four times the sample, because the margin falls with √n. Leave the expected result at 50% unless you have real prior data, because p(1−p) is largest there: the 50% assumption produces the biggest sample and therefore cannot under-deliver whatever the true split turns out to be. The population size is usually irrelevant and this surprises people every time. Sampling 1,068 people gives ±3 points whether the population is fifty thousand or fifty million; the correction only bites once you are sampling more than roughly 5% of a small population, which is why it is optional here. Two practical warnings. The number this returns is COMPLETED responses, not invitations — at a 20% response rate you need to contact five times as many people to land it. And it sizes random sampling error alone. A perfectly sized sample drawn from the wrong frame, or one where the people who declined differ systematically from those who answered, is precisely wrong rather than roughly right, and no increase in n repairs either problem.