Sample Size Calculator

Work out how many responses you need for a survey or study to hit a target margin of error at a chosen confidence level, for estimating a proportion or a mean, with a finite population correction.

Sample size needed
385
Before rounding
384.15
z*
1.96

Step-by-step working

  1. z* for 95% confidencez* = 1.96
  2. n₀ = z*² · p(1 − p) ÷ E²1.96² × 0.5 × 0.5 ÷ 0.05² = 384.15
  3. Always round up to the next whole personn = 385

This is the number of completed responses. If you expect a 20% response rate, invite about five times as many people.

Formula proportion: n = z*² · p(1 − p) ÷ E² mean: n = (z* · σ ÷ E)²

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An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

The famous 385

For ±5% at 95% confidence with an unknown proportion (use 50%): n = 1.96² × 0.25 ÷ 0.05² = 384.16, rounded up to 385. That is why so many surveys aim for about 400 responses. For ±3% you need 1,068.

Small populations

If the population is small, you need fewer responses. For a school of 600 students, the 385 above becomes 385 ÷ (1 + 384 ÷ 600) ≈ 235. Enter the population size to apply this correction.

For a mean, you need an estimate of σ, from a pilot study, earlier research, or range ÷ 4 as a rough guess.

Frequently asked questions

Why always round up?

Rounding down would give a margin of error slightly larger than your target. You can’t survey a fraction of a person, so take the next whole number.

Does this work for hypothesis tests?

This calculator sizes a study for estimation precision. Sizing for a hypothesis test also needs a target effect size and power (often 80%), which is a different calculation.