Free research tool
Power analysis calculator
How many participants does your study need? Pick your test, effect size, α and target power to get the required sample size. Or go the other way: the power of a fixed sample, or the smallest effect it can detect. The calculations use the exact noncentral distributions G*Power uses, and run in your browser on any laptop, Mac, Chromebook or phone.
Compute the effect size from your numbers
Required total sample size
128
How it works
Power is the chance that the test statistic lands beyond its critical value when the effect is real. Under the alternative hypothesis the statistic follows a noncentral distribution, and its noncentrality grows with effect size and N:
| Test | Distribution, df | Noncentrality |
|---|---|---|
| Independent t | t, n₁ + n₂ − 2 | δ = d·√(n₁n₂ / (n₁ + n₂)) |
| Paired t | t, N − 1 | δ = d_z·√N |
| One-way ANOVA | F, (k − 1, N − k) | λ = f²·N |
| Regression R² | F, (p, N − p − 1) | λ = f²·N |
| Chi-square | χ², df | λ = w²·N |
| Correlation | exact distribution of r under a bivariate normal model | |
The required N is the smallest whole number whose exact power reaches your target. As in G*Power, ANOVA assumes equal group sizes, and a t-test with unequal allocation uses n₂ = ⌈ratio × n₁⌉. Correlation power uses the exact (not Fisher-z) distribution, which is G*Power's "Exact – bivariate normal model". That is why r = .3 needs N = 84 here, where the Fisher-z approximation gives 85.
Every calculation runs in your browser. The engine is checked against G*Power 3.1 reference results and R's pwr package, e.g. d = 0.5 → 64 per group, f = 0.25 with 3 groups → 159, f² = 0.15 with 3 predictors → 77, w = 0.3 with df = 1 → 88.
Frequently asked questions
What is statistical power?
Power (1 − β) is the probability that your test gives a significant result when an effect of the size you assumed really exists. A study with 50% power misses a true effect half the time, and the effects that underpowered studies do detect tend to be exaggerated. That is why reviewers and ethics committees ask for a power analysis before data collection.
Why is 0.80 the usual target for power?
It is Jacob Cohen’s (1988) convention. It accepts a 20% risk of a Type II error, four times the 5% Type I risk at α = .05, on the view that a false positive is usually costlier than a missed effect. It is a convention, not a rule. Use .90 or .95 when missing a real effect is costly (clinical or policy studies) or when participants are cheap to recruit.
What are small, medium and large effect sizes, and should I use them?
Cohen’s benchmarks are d = .2/.5/.8 for t-tests, f = .10/.25/.40 for ANOVA, f² = .02/.15/.35 for regression, r = .1/.3/.5 for correlation, and w = .1/.3/.5 for chi-square. Cohen meant them as a last resort for when nothing better is known. A better basis is the effect reported in prior studies or meta-analyses in your area, or the smallest effect that would matter in practice. Typical effects vary a lot between fields, and "medium" is often optimistic.
Should I calculate power after my study (post-hoc power)?
Not with the effect size you observed. "Observed power" is a direct function of the p-value (p = .05 corresponds to roughly 50% power), so it adds no information and cannot explain a non-significant result. Plan N a priori. After the study, report confidence intervals, or run a sensitivity analysis showing the smallest effect your sample could reliably detect. The "for a given sample size" modes here are meant for planning with a fixed budget, using an effect size chosen in advance.