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Survey Sample Size Calculator

This survey sample-size calculator applies Cochran’s (1977) classic formula n = z² · p · (1 − p) / e² to find the minimum number of respondents needed for a poll or questionnaire at a chosen confidence level and margin of error. Pick a confidence level from 80% to 99.9%, set the margin of error e and the expected proportion p (use 50% when unsure — it is the most conservative value), and optionally enter the population size N to apply the finite-population correction (FPC). You get a sample size (rounded up), the z value used and the infinite-population baseline — everything researchers, market analysts and students need before fielding a survey.

Required sample size

385

Treated as an infinite population (no FPC).

z value used

1.96

Infinite-population baseline

385

Formula: n = z² · p · (1 − p) / e², with z from the confidence level and p, e expressed as decimals.

Formula

n₀ = z² · p · (1 − p) / e² n = n₀ / (1 + (n₀ − 1) / N) (apply when a finite population N is known)

Frequently asked

Why do public opinion polls almost always survey around 1,000 people?

At 95% confidence with a ±3% margin and p = 50%, the infinite-population formula gives n₀ ≈ 1,068. Around 1,000 respondents is enough to keep the margin of error near ±3% for any large country or region, which the media regards as acceptable accuracy. Doubling the sample only narrows the margin slightly while doubling cost and field time — diminishing returns set in fast above 1,000.

What is the difference between margin of error and confidence level?

They measure two different aspects of sampling error. The margin of error e (±%) is the maximum distance you will tolerate between estimate and true value. The confidence level (%) is the probability — across many hypothetical repeats — that the interval actually contains the true value. “95% confidence, ±5%” means that if you repeated the survey 100 times, in roughly 95 of them the estimate would be within 5 pp of the true proportion. Tightening either dial inflates the required sample size geometrically.

When should I enter the population size N?

Enter N only when the universe is finite and relatively small. The finite-population correction starts to matter once N drops below roughly 10,000 — surveying all 500 employees of one company, 1,200 students at one school, or 800 households in a complex. The smaller the population relative to the sample, the more you save. For huge populations (all adults in a country, all global users of a product) leaving N blank is equivalent to entering it, because the correction term collapses to 1.

How do stratified or cluster sampling change the required sample size?

This tool assumes simple random sampling (SRS). Real-world surveys often use stratified, cluster, or multi-stage designs and you must multiply the SRS figure by the design effect deff = Var(design) / Var(SRS). In social-science fieldwork deff is commonly 1.2–2 — so the actual sample must be 1.2–2× the value reported here. You must also inflate for non-response: if you expect 70% to reply, divide the SRS sample by 0.7 to set the invite count. Some efficient designs (e.g. PPS sampling) can pull deff below 1, but they require more sophisticated estimators downstream.

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