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Sample size calculation

Power calculator

Calculate how many people you need to detect an effect, or how much power the sample you already have provides.

Statistical test

What do you want to calculate?

Sample size (a priori) Power (post hoc)

Effect size

Significance level (α)

The probability of a type I error you accept. 0.05 is typical.

Tails

Use one tail only if your hypothesis states the direction of the effect.

Number of groups

Number of predictors

Desired power (1 − β)

Probability of detecting the effect if it exists. 0.80 is typical.

Size ratio (n2 / n1)

1 = groups of the same size.

Total sample size (N)

Group 1 size

Group 2 size

Result

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How is it calculated?

It uses the same methods as G*Power (Faul et al., 2007), based on noncentral distributions:

Student's t: noncentral t distribution with δ = d·√(n₁n₂/(n₁+n₂)) for independent groups and δ = d·√n for paired samples or one sample.
Correlation: exact distribution of the coefficient r under the bivariate normal model, with ρ₀ = 0.
One-way ANOVA: noncentral F with λ = f²·N and equal group sizes.
Multiple linear regression: noncentral F with λ = f²·N to test that R² is different from zero.

The Small, Medium and Large buttons use Cohen's (1988) reference values. Whenever possible, base the effect size on previous studies on your topic.

How to cite this tool

AtheneaLab. (2026). Power calculator [Web application]. https://athenealab.com/en/sample-size/power/

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