Effect Size Calculator (Cohen's d)

Measure how big the difference between two group means is, in standard deviations, with Cohen's d and Hedges' g.

Two groups

Group 1

Mean

Std dev

Group 2

Mean

Std dev

Cohen's d

0.628

Hedges' g

0.619

Size

medium

Pooled s = √[((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2)] = 11.139

d = (x̄₁ − x̄₂) ÷ s = (82 − 75) ÷ 11.139 = 0.628

g = d × [1 − 3 ÷ (4(n₁+n₂) − 9)] = 0.619

Approx. 95% CI for d: 0.085 to 1.172 (SE ≈ 0.2774)

The group means differ by 0.63 pooled standard deviations, a medium effect by Cohen's rough benchmarks (0.2 small, 0.5 medium, 0.8 large). If both groups are roughly normal with equal spread, there is about a 67.2% chance that a randomly chosen person from the higher-mean group scores above a randomly chosen person from the other group.

How to use this tool

Enter the mean, standard deviation, and sample size for each of the two groups.
The calculator pools the two standard deviations and divides the difference in means by that pooled value.
Read Cohen's d, the small-sample corrected Hedges' g, and the approximate 95% confidence interval.
Use the size label and the "chance of superiority" statement to put the number in words.

Formula Reference

Cohen's d

d = (x̄₁ − x̄₂) ÷ s_pooled

Pooled standard deviation

s_p = √[ ((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2) ]

Hedges' g

g = d × [ 1 − 3 ÷ (4(n₁+n₂) − 9) ]

SE of d (approx.)

√[ (n₁+n₂)/(n₁n₂) + d²/(2(n₁+n₂)) ]

ArticleEffect Size Explained ArticleStatistical Power Articlet-Tests Calct-Test Calculator CalcSample Size Calculator GlossaryGlossary: Cohen's d

Frequently Asked Questions

What is a good Cohen's d?+

Cohen suggested 0.2, 0.5, and 0.8 as rough benchmarks for small, medium, and large effects. These are conventions, not rules. What counts as large depends on the field and the stakes.

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

Cohen's d slightly overestimates the effect in small samples. Hedges' g applies a correction factor that shrinks it a little. With samples above about 50 per group, the two are almost identical.

Why report an effect size as well as a p-value?+

A p-value says whether a difference is detectable, and it depends heavily on sample size. An effect size says how big the difference is, independent of sample size. A huge sample can make a trivial difference significant.

What is the "chance of superiority"?+

It is the probability that a randomly chosen member of one group scores higher than a randomly chosen member of the other, computed as Φ(d ÷ √2). It assumes both groups are roughly normal with equal spread.

How to use this tool

Enter the mean, standard deviation, and sample size for each of the two groups.

The calculator pools the two standard deviations and divides the difference in means by that pooled value.

Read Cohen's d, the small-sample corrected Hedges' g, and the approximate 95% confidence interval.

Use the size label and the "chance of superiority" statement to put the number in words.