Calculators
Statistical Power Calculator
Find the sample size per group needed to detect a difference between two means or two proportions, and the power achieved with a given sample.
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The tool
Enter your numbers below. Results update as you type, and nothing leaves your browser.
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What people use it for
- A/B test planning
- Clinical and academic study design
- Grant proposals
- Checking whether a null result was underpowered
About this tool
What the Statistical Power Calculator does
Statistical power is the chance a study detects an effect that really exists. It depends on the effect size, the significance level (α), whether the test is one- or two-sided and the sample size. This calculator uses the normal approximation for comparing two independent groups.
It also works as a power analysis calculator or a sample size for two groups.
Formula
- Means: n = 2 × ((z₁₋α/k + z₁₋β) ÷ d)² per group, k = number of tails
- Proportions: n = (z₁₋α/k √(2p̄q̄) + z₁₋β √(p₁q₁ + p₂q₂))² ÷ (p₁ − p₂)²
Worked example
Using the starting values in the calculator above:
| Input | Value |
|---|---|
| Comparison | Two proportions |
| Effect size (Cohen’s d) | 0.5 |
| Proportion in group 1 | 10% |
| Proportion in group 2 | 13% |
| Significance level (α) | 5% |
| Test | Two-sided |
| Target power | 80% |
| Your sample per group (for achieved power) | 1,000 |
| Result | Value |
|---|---|
| Sample size per group | 1,774 |
| Power with your sample | 55.7% |
| Total sample (both groups) | 3,548 |
| Effect to detect | 3.00 points (30.0% relative) |
How to read the result
Decide the smallest effect worth detecting before collecting data, not after.
Small samples give t-test results slightly less powerful than this normal approximation; add a few per group for very small studies.
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Questions
Questions about this tool
The things clients actually want to know — costs, timelines, ownership and what happens after launch.
The probability of detecting a real effect of a given size; 80% is a common target.
The difference between two means divided by their pooled standard deviation.
Required sample size grows with the inverse square of the effect size.
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