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Cohen's d Effect Size Calculator

Cohen's d from two group means and standard deviations, with the pooled standard deviation (weighted by sample size when you enter n), Hedges' g small-sample correction, and the overlap, U3 and common-language effect size that say what the number means in practice.

Last updated: October 2026

Cohen's d

0.333

Formula below · 3 sources (ncbi.nlm.nih.gov, doi.org, apa.org) · Updated Oct 2026

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About this calculator

Cohen's d is the standardised difference between two means: d = (M₁ − M₂) ÷ s_pooled. Dividing by the pooled standard deviation puts the difference in SD units, so effects measured on different scales (test points, millimetres of mercury, seconds) can be compared and combined in meta-analysis, and it answers the question a p-value cannot: not whether the groups differ, but by how much. With sample sizes entered, the pooled SD is the degrees-of-freedom-weighted root mean square, s_pooled = √[((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2)], the form Cohen defined and the one used by t-tests. Without them the calculator uses the unweighted root mean square √[(s₁² + s₂²) ÷ 2], which is identical when the groups are the same size. Hedges' g applies the small-sample correction factor J = 1 − 3 ÷ (4(n₁ + n₂) − 9) to remove d's slight upward bias; it matters below about 20 per group and is the version most journals and meta-analysis software report. Three further tiles translate d into plain language under the usual assumption of normal distributions with equal variances: Cohen's U3 = Φ(d) is the percentage of group 2 that lies below the mean of group 1; the overlap 2Φ(−|d|/2) is the share of the two distributions' area that they have in common; and the common-language effect size Φ(d/√2) is the probability that a randomly chosen member of group 1 scores higher than a randomly chosen member of group 2 (McGraw and Wong 1992). Cohen's benchmarks of 0.2, 0.5 and 0.8 for small, medium and large effects are conventions he offered reluctantly; what counts as meaningful depends on the field, the cost of the intervention and the outcome (a d of 0.2 on mortality is enormous). The sign of d follows the order of the means; report it as given or state which group is higher. For two proportions use an odds ratio or number needed to treat instead, and for correlations use r.

How to use

Example 1 — the defaults: group 1 mean 105, group 2 mean 100, both SDs 15, 30 per group. Pooled SD = √[(29 × 225 + 29 × 225) ÷ 58] = √225 = 15, so d = (105 − 100) ÷ 15 = 0.333: a small-to-medium effect. Hedges' g = 0.333 × (1 − 3 ÷ (4 × 60 − 9)) = 0.333 × 0.987 = 0.329. U3 = Φ(0.333) = 63.1%, overlap = 2Φ(−0.167) = 86.8%, common-language effect size = Φ(0.236) = 59.3%. Example 2 — unequal groups: means 110 and 100, SDs 18 and 22, with 20 and 40 participants. Pooled SD = √[(19 × 324 + 39 × 484) ÷ 58] = √[(6,156 + 18,876) ÷ 58] = √431.6 = 20.77, so d = 10 ÷ 20.77 = 0.481. Leave the sample sizes blank and the unweighted pooled SD √[(324 + 484) ÷ 2] = 20.10 gives d = 0.497 instead; the weighted figure is the correct one when the groups differ in size. Both are medium effects by Cohen's scale.

Frequently asked questions

What is the formula for Cohen's d?

d = (M₁ − M₂) ÷ s_pooled, where s_pooled = √[((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2)]. When the two groups are the same size this reduces to √[(s₁² + s₂²) ÷ 2], which is what the calculator uses if you leave the sample sizes blank.

How do I interpret the value of Cohen's d?

Cohen's rule of thumb is 0.2 small, 0.5 medium, 0.8 large. A d of 1.0 means the means differ by a full standard deviation. The tiles give more concrete readings: at d = 0.5, 69% of the comparison group scores below the first group's mean, the distributions overlap by 80%, and a random member of group 1 outscores a random member of group 2 64% of the time. Whether that is important depends on the outcome and the cost of achieving it.

What is the difference between Cohen's d and Hedges' g?

They are the same statistic with different bias handling. d is slightly too large in small samples; Hedges' g multiplies it by J = 1 − 3 ÷ (4(n₁ + n₂) − 9), which is 0.987 for 30 per group and 0.96 for 10 per group. For samples over about 20 per group the two agree to the second decimal. Meta-analyses almost always use g.

What is the difference between effect size and statistical significance?

A p-value says whether a difference is unlikely to be chance given the sample size; an effect size says how big it is. With 10,000 participants a trivial d of 0.03 is highly significant, and with 15 participants a large d of 0.9 may not be. Reporting both is now standard practice (the APA Publication Manual asks for effect sizes), and d is also the input to a power analysis for the sample size of a future study.

Can Cohen's d be negative?

Yes. The sign just reflects which mean you entered first: swapping the groups changes 0.33 to −0.33. The size of the effect is |d|, which the bands and the overlap tile use. By convention many papers report d so that a positive value favours the treatment group, so state the direction in words.

When should I not use Cohen's d?

When the outcome is binary (use an odds ratio, risk difference or number needed to treat), when the two groups have very different variances (use Glass's Δ with the control group's SD), for paired or repeated-measures designs (the SD of the differences or the pre-test SD gives a different d), and for heavily skewed data, where the overlap and U3 readings assume normality and can mislead.

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