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Sample size calculator for comparing two groups (power analysis)

Planning an experiment or RCT with two arms? Enter the smallest effect size worth detecting, your α and desired power, and get the participants needed per group.

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Benchmarks: 0.2 small, 0.5 medium, 0.8 large. Use the smallest effect that would still matter.

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When to use this

Use this at the design stage of any two-arm study — treatment vs. control, intervention vs. usual care, condition A vs. condition B — where the outcome is continuous and will be tested with an independent samples t-test. Funders, ethics boards, and preregistration templates all expect exactly this calculation: the sample size follows from the smallest effect size you care about, your α, and the power you want. Base the expected d on a pilot study, a meta-analysis in your area, or the smallest effect that would be practically meaningful — not on hope.

Key assumptions

  • Two independent groups of equal size, continuous outcome, t-test analysis.
  • The effect size entered is in standard deviation units (Cohen’s d).
  • Normal-approximation formula with a small-sample correction — matches G*Power within a participant or two.

Common mistakes

  • Powering for the effect you found in a small pilot — pilot effect sizes are noisy and usually inflated.
  • Ignoring attrition: recruit above n to end with n analyzable participants.
  • Running a "post-hoc power" analysis on a completed study — it adds no information beyond the p-value.

Frequently asked questions

What effect size should I enter if I have no pilot data?
Use the smallest effect size of interest (SESOI): the smallest difference that would still matter clinically or practically. If truly nothing is known, d = 0.5 ("medium") is a common planning default in the social sciences, but be aware that many published effects are closer to d = 0.2–0.4 — powering for those requires several hundred participants per group.
Why 80% power?
Convention, dating to Cohen: it fixes the ratio of Type II to Type I error at 4:1. Trials with expensive or irreversible consequences increasingly use 90% or 95%. Below 80%, a null result is hard to interpret — the study could not reliably have found the effect even if it existed.
Does this work for a Mann–Whitney U test or unequal groups?
Approximately. For a Mann–Whitney analysis of roughly normal data, multiply n by 1.16 (its asymptotic relative efficiency). For unequal allocation r = n2/n1, the total N grows by a factor of (1+r)²/(4r) — e.g. a 2:1 split needs about 12% more participants overall.

Related free tools

Sample size calculatorEffect size (Cohen's d)Confidence intervalDescriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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