Power & Sample-Size Calculator
The single most valuable calculation in statistics happens before you collect a single data point: how many participants do you actually need? Pick your test, choose what you want to solve for, and read the answer off the power curve — with exact noncentral math, not normal-approximation shortcuts.
⚡ Power & sample-size calculator
Fix any two of {effect size, sample size, power} and solve for the third. The curve is power vs. sample size; the marker sits at the operative point.
How to use it
- Planning a study? Keep "Solve for → Sample size", enter the effect size you'd hate to miss and the power you want (0.80 is the convention), and read off the n. That's an a priori power analysis — the calculation you should run before collecting data.
- Already have a fixed n? Switch to "Power" to see your chance of detecting an effect of a given size — or to "Effect size" for the minimum detectable effect: the smallest effect this design can reliably catch.
- Watch the punishing curve. Halving the effect you're chasing roughly quadruples the sample you need. A large effect needs a couple dozen per group; a small one can demand hundreds.
These are exact power values, not normal-curve approximations. The t, ANOVA, and chi-square scenarios use the true noncentral t, F, and χ² distributions; correlation uses the exact bivariate-normal distribution of r. Results match G*Power to within rounding. The two-proportions test is the one deliberate exception — it uses the standard arcsine (Cohen's h) normal approximation, which is why it's labeled approximate. ANOVA and chi-square are naturally one-tailed (the F/χ² rejection region is the upper tail), so no tail choice is offered.
Effect-size benchmarks (Cohen, 1988)
| Test | Metric | Small | Medium | Large |
|---|---|---|---|---|
| t-test | d | 0.20 | 0.50 | 0.80 |
| Correlation | r | .10 | .30 | .50 |
| ANOVA | f | 0.10 | 0.25 | 0.40 |
| Chi-square | w | 0.10 | 0.30 | 0.50 |
| Proportions | h | 0.20 | 0.50 | 0.80 |
Benchmarks are a last resort — Cohen said so himself. Whenever you can, power for the smallest effect that would still matter, or an effect from prior literature discounted for publication bias. Translate between d, r, η² and the rest with the effect-size converter.
Where this comes from
- Effect size & power — the core intuition, one interactive at a time. See the Stats 1 lesson →
- Power analysis for complex designs — using power as a planning tool, and what to do when formulas run out. See the Stats 3 lesson →
- Need the critical values behind these curves? The tables & calculators page has exact z, t, χ² and F. The formula sheet lists every formula these tests are built from.
Not sure which test to power for? The Plan My Analysis wizard walks you from your research question to the right test and its sample size — the same exact math as this page — then hands you a printable plan for your supervisor. Plan your analysis →