Power & Sample-Size Calculator
One of the most useful calculations in statistics comes before you collect any data: how many participants do you need? Pick your test, choose what you want to solve for, and read the answer off the power curve, computed 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 shows power against sample size, and the marker shows your current setting.
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 how steep the curve is. Halving the effect you want to detect needs roughly four times the participants. Two dozen per group may be enough for a large effect; a small one runs into the 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, so it is 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 |
Cohen himself treated his benchmarks as a last resort. 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 3 lesson →
- Power analysis for complex designs uses power as a planning tool, and covers what to do when the 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 takes you from your research question to the right test and its sample size, using the same exact math as this page. It ends with a printable plan for your supervisor. Plan your analysis →