Study design

Sample Size & Power Calculator

Too few subjects and a study misses real effects; too many and it wastes time and money. This tool plans the middle: how many subjects you need, what chance your study has of catching a real effect (its power), and the smallest difference it can honestly detect.

How it works

To detect an effect, the sample size follows from three choices: the smallest difference worth catching (Δ), the significance level (α), and the power you want. For two groups of averages, n per group = 2·((z_crit + z_power)·σ/Δ)². To estimate a value within a margin of error E, the companion post's formula applies: n = (zσ/E)² for an average, and n = z²p(1−p)/E² for a percentage.

Everything uses the normal approximation (z-values). That is accurate for moderate and large samples; for very small samples, t-based software such as R's pwr asks for a subject or two more — if your answer here is under ~30 per group, treat it as a floor, not a ceiling. All math runs client-side and is verified against published reference values — see Software & sources.

Companion explainer: Sample Size Matters: Understanding the Power of Representative Data on Solved By Stats — why a study's conclusions are only as good as its sample, and how power, Type I and Type II errors trade off. Same lesson, other posts: The Importance of Sample Size in Statistical Studies · Why Sample Size Matters for Study Conclusions · Sample Size Sensitivity · Assessing the Impact of Sample Size on Study Conclusions · The Role of Sample Size in Study Conclusions · The Importance of Sample Size for Study Conclusions · Study Size Sensitivity · The Importance of Sample Size in Study Conclusions.