Power Analysis Calculator
Compute sample size and statistical power yourself, instantly. Pick your test, enter the values — see the result with a full sensitivity analysis and downloadable charts.
Give a target power → we compute the sample size needed.
Required sample
Power delivered by this sample: 80.1%
Interpretation
To detect an effect of d = 0.5 at α = 0.05, two-sided with a independent two-sample t-test at 80% power, you need Group 1 n₁ = 63, Group 2 n₂ = 63 (total N = 126). In the same study, reaching 90% power needs a total of 170, and 95% needs 208.
Power curve
How power rises as the sample grows — dashed lines mark 80% power and your scenario.
Type I (α) and Type II (β) error
Distributions under H₀ (no effect) and H₁ (expected effect). Beyond the critical value is Type I error (α); the region of H₁ below it is Type II error (β); power = 1 − β.
Sensitivity: total N needed under different assumptions
Unsure about the effect size? See the sample needed for neighbouring scenarios too. Your row is highlighted.
| Scenario | 80% | 90% | 95% |
|---|---|---|---|
| d = 0.2 | 786 | 1052 | 1300 |
| d = 0.3 | 350 | 468 | 578 |
| d = 0.5 | 126 | 170 | 208 |
| d = 0.8 | 50 | 66 | 82 |
Mean, proportion and correlation tests use the large-sample (normal) approximation; ANOVA, chi-square and regression use exact central/noncentral F and χ² distributions. For small samples or complex designs, we prepare the justified report.
Need a publication-ready, justified report?
For ethics boards and theses, we'll pick the right test and assumptions and prepare your justified sample-size report.
What is power analysis?
Power analysis determines a study's probability of detecting a real effect (its statistical power) and the sample size needed to achieve it. Most theses and ethics-board applications require an a priori power analysis and a justified sample size before data collection.
How do you do a power analysis?
To do a power analysis you choose your test (two-sample t-test, ANOVA, chi-square, correlation, regression, etc.), the expected effect size, the significance level (α) and the target power (usually 80%). Enter these and the calculator returns the required sample size — or the power your current sample delivers — instantly.
How is sample size calculated?
Sample size calculation depends on effect size, α and desired power: the smaller the effect or the higher the power, the larger the sample. The sensitivity table below also shows the sample needed for neighbouring scenarios when you're unsure of the effect size.
Frequently asked questions
Is the power analysis calculator free?
Yes, this power analysis and sample size calculator is completely free and runs instantly in your browser.
Which tests can I run a power analysis for?
You can compute power and sample size for two independent/paired means, one sample, two/one proportions, correlation, one-way ANOVA, chi-square and multiple regression.
What if I don't know my effect size?
Use the small/medium/large presets, or compare the sample needed under different assumptions in the sensitivity table. If you're unsure, we prepare the justified report for you.