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Cohen's d Calculator

Measure effect size between two groups with Cohen’s d from their means, standard deviations and sizes — with the pooled SD and a magnitude label.

Group 1 mean

Group 1 standard deviation

Group 1 size (n₁)

Group 2 mean

Group 2 standard deviation

Group 2 size (n₂)

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How it works

pooled SD = √( ((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2) ) · d = (mean₁ − mean₂) ÷ pooled SD

Cohen’s d expresses the difference between two group means in units of their pooled standard deviation, giving a scale-free measure of effect size that a p-value alone cannot. The pooled SD combines both groups’ spreads, weighted by their degrees of freedom, so a d of 1 means the means are a full standard deviation apart. Cohen’s rough benchmarks call 0.2 small, 0.5 medium and 0.8 large, but they are guidelines — what counts as meaningful depends on the field.

Worked example

With group 1 at mean 100, SD 15, n = 30 and group 2 at mean 90, SD 15, n = 30, the pooled SD is √(((29·225)+(29·225)) ÷ 58) = √225 = 15. Then d = (100 − 90) ÷ 15 ≈ 0.667 — a medium effect, meaning the groups differ by about two-thirds of a standard deviation.

Sources: Effect size (Cohen’s d) — Wikipedia

Frequently asked questions

What is a "large" effect size?

Cohen suggested d ≈ 0.2 as small, 0.5 as medium and 0.8 as large, and this calculator labels the result on that scale. They are conventions, not laws — in some fields a d of 0.3 is a big deal, in others 0.8 is routine, so always interpret against context.

How is Cohen’s d different from a p-value?

A p-value tells you whether a difference is likely real; Cohen’s d tells you how big it is. A huge sample can make a trivial difference statistically significant, so reporting the effect size alongside the p-value is what shows whether the difference actually matters.

Why divide by a pooled standard deviation?

Pooling combines the spread of both groups into a single yardstick, so the difference in means is measured on a common scale. Weighting each group’s variance by its degrees of freedom (n − 1) gives the more reliable estimate when the two sample sizes differ.

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