Calculators
Statistical Power Calculator
Calculate statistical power, required sample size, or minimum detectable effect size for one-sample, two-sample, and paired t-tests locally in your browser.
Choose a t-test type and what to solve for: Power (from sample size and effect size),Sample size (from target power and effect size), or Effect size (from target power and sample size). Effect size uses Cohen's d convention: 0.2 = small, 0.5 = medium, 0.8 = large. Calculations use the non-central t-distribution. All computation is local; your values are not uploaded or stored.
Plan your study with adequate power to detect meaningful effects.
Statistical power is the probability of correctly rejecting a false null hypothesis. This calculator solves for power, sample size per group, or minimum detectable effect size (Cohen's d) for one-sample, two-sample (equal or unequal variances), and paired t-tests. Power = 1 − β, where β is the Type II error rate. Conventional thresholds: 0.80 is adequate, 0.90 is strong. Cohen's d benchmarks: 0.2 = small, 0.5 = medium, 0.8 = large. The non-central t-distribution computes exact power. For example, a two-sample test with α = 0.05 (two-tailed), n = 30 per group, and d = 0.5 gives power ≈ 0.478; to reach 0.80 power with d = 0.5 requires n ≈ 64 per group; with n = 30 and target power 0.80, the minimum detectable d ≈ 0.72. All calculations run locally in your browser; your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is statistical power?
Statistical power (1 − β) is the probability of correctly rejecting a false null hypothesis. It is the chance your test will detect an effect if one truly exists. Conventional thresholds: 0.80 (80%) is considered adequate, 0.90 (90%) is strong. Low power means you risk missing real effects (Type II error).
What is Cohen's d?
Cohen's d is a standardized effect size: the difference between means divided by the pooled standard deviation. For one-sample and paired tests, d = (mean − hypothesized) / SD. For two independent samples, d = (mean₁ − mean₂) / SD_pooled. Common benchmarks: 0.2 = small, 0.5 = medium, 0.8 = large, but interpret in your research context.
What does "solve for" mean?
Choose what you want to find: Power — compute the power from your sample size and effect size (post-hoc). Sample size — find the minimum n per group to achieve a target power (a priori). Effect size — find the smallest d you can detect with your n and target power (minimum detectable effect).
When should I use one-tailed vs two-tailed?
Use two-tailed (the default) unless you have a strong, pre-specified directional hypothesis and are only interested in effects in one direction. One-tailed tests have more power for the same sample size but double the Type I error rate in the specified direction if the true effect is opposite.
How does the calculator compute power?
Power is the probability that the non-central t-distribution exceeds the critical value. The non-centrality parameter is d × √n for one-sample and paired tests, and d × √(n/2) for two-sample tests with equal variances (pooled). The cumulative distribution function uses a series expansion with the regularized incomplete beta function. For large degrees of freedom, a normal approximation is used.
Are my values uploaded?
No. All calculations run locally in your browser. CodeASystem does not upload or store your input values.