Sample Size Calculator

Calculates how many responses or samples a survey or experiment needs for a given confidence level, margin of error or power. Use it to decide how many people to survey, or how many subjects each group needs.

How to use

1. Choose a tab: "Proportion (survey)", "Mean", "Compare two means" or "Compare two proportions".
2. For a survey, enter the "Confidence level", "Margin of error (±)" and "Expected proportion", and the "Population size (optional)" if the group is a known number.
3. To compare two groups, set the effect size (or mean difference and standard deviation), "Significance level α", "Power" and "Test direction".
4. To get the margin of error for a given sample size, switch "Solve for" to "Margin of error".

How it works

• For a proportion, n₀ = z² × p(1 − p) ÷ e². With a population size N, n = n₀ ÷ (1 + (n₀ − 1) ÷ N). Results are rounded up.
• For two means, the power of the two-sample t-test is computed with the non-central t distribution, and the smallest n per group that reaches the target is shown.
• Simple random sampling is assumed; response rate and dropout are not included. See "Formula and assumptions" for details.

Questions and answers

What sample size do I need for a survey?

At 95% confidence, ±5% margin of error and 50% expected proportion: 1.96² × 0.25 ÷ 0.05² ≈ 384.2, so 385. For ±3% you need 1,068.

Does a small population need a smaller sample?

Yes. With the same settings and a population of 1,000, the finite population correction gives 278. For a very large population, size hardly matters.

What expected proportion should I use if I do not know it?

Use 50%. p(1 − p) is largest there, so it gives the largest, safest sample size.

How many subjects per group do I need to compare two groups?

With effect size d = 0.5, α = 0.05, 80% power and a two-sided test, 64 per group. Smaller effects need more.