Cohen's d calculator (with Hedges' g)

What this calculates

Cohen's d is the standardized mean difference (SMD) between two independent groups: the difference in their means expressed in pooled standard-deviation units. It lets you compare an effect measured on one scale against an effect measured on another, which is why it is the workhorse effect size for meta-analysis when trials report continuous outcomes on different instruments.

This calculator takes each group's mean, standard deviation, and sample size, then reports d, the bias-corrected Hedges' g, and the 95% confidence interval of g. Everything recomputes live and the full derivation sits behind the "Show steps & citation" toggle.

The formulas

The pooled SD uses the Cochrane Handbook §6.5.1.2 form, then d is the mean difference over that pooled SD:

s_pooled = √( ((n₁−1)·s₁² + (n₂−1)·s₂²) / (n₁+n₂−2) )
d = (m₁ − m₂) / s_pooled

Cohen's d is upwardly biased in small samples. Hedges' g applies the correction factor J (df = n₁+n₂−2), and its variance gives the confidence interval:

J = 1 − 3 / (4·df − 1)
g = J · d
Var(g) = (n₁+n₂)/(n₁·n₂) + g² / (2·(n₁+n₂))
95% CI = g ± 1.96·√Var(g)

When it is valid (and when it is not)

This method assumes two independent groups with continuous outcomes and reasonably comparable within-group variances (the pooled SD presumes both arms estimate a common spread). It is the correct tool for a parallel-group RCT reporting post-intervention means and SDs per arm.

Do not use it for paired or crossover designs, where the relevant SD is the SD of the within-person differences, not the pooled between-group SD. That needs the paired formula (Cochrane §23.2.7.2). If a trial reports standard errors rather than SDs, convert first (SD = SE·√n). And when n₁+n₂ is below 20 the calculator flags that the J correction is material: report g, not d. For samples in the hundreds, d and g converge and the distinction stops mattering.