Power & Sample Size Calculator
Calculate the required sample size for a two-sample t-test from an expected effect size, or compute the statistical power of your planned study. Free online tool with the 0.80 convention.
What Are Power and Sample Size?
Statistical power is the probability that a study detects an effect of a given size when that effect truly exists (1 − β). The conventional target is 0.80: a study should have an 80% chance of finding the effect it is designed to find.
Required sample size depends on three ingredients: the expected effect size (the smaller the effect, the more participants you need), the significance level α, and the desired power. Planning sample size before collecting data avoids both underpowered studies, which waste participants and miss real effects, and overpowered ones, which are costly and can turn trivial effects into "significant" results.
Cohen's benchmarks for d are a useful starting point: d ≈ 0.2 is small, 0.5 medium and 0.8 large. Use pilot data or prior literature to choose the value that is meaningful in your field.
Key Formulas
For a two-sample t-test, the test statistic under the alternative follows a noncentral t distribution with noncentrality δ. Power is the probability that this statistic exceeds the critical value:
δ = d × √(n₁n₂ / (n₁+n₂))
power = P(|t'| > t_crit)
How to Use This Calculator
Follow these steps:
- Estimate the expected effect size (Cohen's d) from prior literature or a pilot study.
- Choose a significance level (typically 0.05) and a desired power (typically 0.80).
- Read the required sample size per group, or switch to the Power tab to check the achieved power of your planned sample sizes.
Worked Example
You expect a medium effect (d = 0.5) and want 80% power at α = 0.05:
Frequently Asked Questions
Have another question? Let us know.
What is statistical power and why does 0.80 matter?
Power is the probability of detecting an effect that truly exists. The 0.80 convention means accepting a 20% chance of missing a real effect (Type II error). Journals and preregistrations commonly require planned analyses to reach 0.80 or higher.
What effect size should I enter?
Use the smallest effect that would be theoretically or practically meaningful in your field. Common starting points are Cohen's benchmarks (0.2 small, 0.5 medium, 0.8 large), but the best source is prior literature or a pilot study on the same measure.
Why does the sample size calculator return an even number?
The tool assumes two groups of equal size, so the per-group n must be a whole number and the total N is twice that. The result is the smallest n at which the exact (noncentral t) power reaches the target.
Can I use this calculator for one-sample or paired designs?
This version covers the two-sample independent t-test, the most common design in psychology. Paired and one-sample designs need roughly half the total sample size; use dedicated software such as G*Power for those cases.
