Power Calculator
The Odds of Catching a Real Effect
Statistical power is the probability of correctly rejecting the null hypothesis when a real effect actually exists — in other words, the chance a study will detect something that is truly there rather than returning an inconclusive, non-significant result. A study with low power can fail to find a genuine effect simply because it wasn't large enough to reliably see it, which is why power is checked before data collection, not after.
The Formula
This calculator uses the two-sample z-test approximation for power:
where d is the effect size (Cohen's d), n is the sample size per group, zα is the critical value for the chosen significance level
How Power Grows With Sample Size
Holding the effect size at a medium d = 0.5 and significance level at α = 0.05 (zα = 1.645):
| Sample size per group (n) | Power |
|---|---|
| 10 | 29.91% |
| 20 | 47.45% |
| 30 | 61.47% |
| 50 | 80.37% |
| 64 | 88.17% |
| 100 | 97.07% |
Values computed directly from the calculator's power formula.
The conventional target of 80% power is reached at roughly n = 50 per group for this effect size and significance level — a benchmark widely used in study planning across psychology, medicine, and A/B testing.
Where This Calculation Matters
- Study planning — researchers calculate expected power before running an experiment to check that the planned sample size can realistically detect the effect they're looking for.
- Grant proposals and protocols — funding bodies and ethics boards frequently require a power analysis before approving a clinical trial or field experiment.
- Interpreting a null result — a non-significant finding from a low-power study is far less informative than the same result from a well-powered one; power tells you how much weight to put on "no effect found."
How to Use This Calculator
- Enter the expected effect size (Cohen's d).
- Enter the sample size per group (n).
- Select the significance level (alpha): 0.10, 0.05, or 0.01.
- Select Calculate to get the estimated statistical power.
Related Calculations
Compute the effect size input first with the Effect Size Calculator, or determine a required sample size directly with the Sample Size for Mean Calculator.