What is the effect size (Cohen’s d)?
Type the mean, standard deviation and size of two independent groups, or the t statistic of their t-test. The effect size calculator gives Cohen’s d, Hedges’ g (corrected for small samples), and whether the effect counts as small, medium or large.
- Cohen’s d
- 1.1269
Cohen’s d is 1.1269 (large effect) and Hedges’ g is 1.0793.
- Hedges’ g
- 1.0793
- Size of the effect
- large
- Correction factor J
- 0.957746
- Difference in means
- 1
- Pooled standard deviation
- 0.88738
Cohen’s d: 1.1269. Cohen’s d is 1.1269 (large effect) and Hedges’ g is 1.0793.
How to calculate
Computes the effect size between two independent groups as Cohen’s d and Hedges’ g, from the two means, standard deviations and sample sizes, or from a t statistic.
Example with the default inputs (From Means and SDs, Mean of group 1 8.7, Standard deviation of group 1 0.82, Size of group 1 10, Mean of group 2 7.7, Standard deviation of group 2 0.95, Size of group 2 10): Cohen’s d is 1.1269 (large effect) and Hedges’ g is 1.0793.
Method: Cohen’s d = (M₁ − M₂) ÷ √[((n₁ − 1)SD₁² + (n₂ − 1)SD₂²) ÷ (n₁ + n₂ − 2)], or d = t × √(1 ÷ n₁ + 1 ÷ n₂); Hedges’ g = d × (1 − 3 ÷ (4(n₁ + n₂) − 9)).
- The two groups are independent (between-subjects), and the standard deviations are sample standard deviations.
- The pooled SD weights each group’s variance by its degrees of freedom, n − 1.
- The size labels are Cohen’s benchmarks for |d| (0.2 small, 0.5 medium, 0.8 large); they are rough guides, not rules.
Worked examples
Each example is checked against the calculator on every build.
- From Means and SDs, Mean of group 1 8.7, Standard deviation of group 1 0.82, Size of group 1 10, Mean of group 2 7.7, Standard deviation of group 2 0.95, Size of group 2 10 gives Cohen’s d 1.126908, Hedges’ g 1.079292, Correction factor J 0.957746, Pooled standard deviation 0.887384, Difference in means 1, Size of the effect large.Source: Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863, formulas 1, 2 and 4 (movie ratings: M = 8.7, SD = 0.82 and M = 7.7, SD = 0.95, n = 10 each; t(18) = 2.52; Cohen’s d_s = 1.13, Hedges’s g_s = 1.08; small 0.2, medium 0.5, large 0.8), https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18)
- From t statistic, t statistic 2.52, Size of group 1 10, Size of group 2 10 gives Cohen’s d 1.126978, Hedges’ g 1.079359, Size of the effect large.Source: Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863, formulas 1, 2 and 4 (movie ratings: M = 8.7, SD = 0.82 and M = 7.7, SD = 0.95, n = 10 each; t(18) = 2.52; Cohen’s d_s = 1.13, Hedges’s g_s = 1.08; small 0.2, medium 0.5, large 0.8), https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18)
- From Means and SDs, Mean of group 1 100, Standard deviation of group 1 15, Size of group 1 30, Mean of group 2 105, Standard deviation of group 2 15, Size of group 2 40 gives Cohen’s d -0.333333, Hedges’ g -0.329643, Correction factor J 0.98893, Pooled standard deviation 15, Size of the effect small.Source: Lakens, D. (2013), Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs, Frontiers in Psychology 4, 863, formulas 1, 2 and 4 (movie ratings: M = 8.7, SD = 0.82 and M = 7.7, SD = 0.95, n = 10 each; t(18) = 2.52; Cohen’s d_s = 1.13, Hedges’s g_s = 1.08; small 0.2, medium 0.5, large 0.8), https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18)
How it works
From means and standard deviations. For two independent groups with means M₁ and M₂, sample standard deviations SD₁ and SD₂, and sizes n₁ and n₂:
- Pooled SD = √[((n₁ − 1) × SD₁² + (n₂ − 1) × SD₂²) ÷ (n₁ + n₂ − 2)]
- Cohen’s d = (M₁ − M₂) ÷ pooled SD
From a t statistic. For an independent-samples t-test: Cohen’s d = t × √(1 ÷ n₁ + 1 ÷ n₂).
Hedges’ g in both cases: J = 1 − 3 ÷ (4(n₁ + n₂) − 9), and g = d × J.
Size of the effect, from |d| (Cohen’s benchmarks): below 0.2 “smaller than small”; from 0.2 to below 0.5 “small”; from 0.5 to below 0.8 “medium”; 0.8 or more “large”.
Exact arithmetic. Typed values are read as exact decimals. d² (the squared difference over the pooled variance, or t² × (n₁ + n₂) ÷ (n₁ × n₂)) and g² = d² × J² are exact fractions; d and g are their square roots with the sign of M₁ − M₂ (or of t), exact when the fraction is a perfect square.
Rules. Means are from −10¹⁵ to 10¹⁵; standard deviations from 0 to 10¹⁵; each group size is a whole number from 2 to 1,000,000,000; t is from −1,000,000 to 1,000,000. When both standard deviations are 0 the pooled SD is 0 and there is no answer. A value too large or too small to hold in a 64-bit float (beyond about 10³⁰⁸, or a nonzero value below about 10⁻³²³) also has no answer, rather than showing infinity or 0. The difference in means and the pooled SD are shown only when working from means.
Output format. d, g, the difference and the pooled SD show 5 significant figures; J shows 6.
Worked examples by hand
Movie ratings (Lakens 2013). M₁ = 8.7, SD₁ = 0.82; M₂ = 7.7, SD₂ = 0.95; n = 10 in each group. Pooled SD = √[(9 × 0.6724 + 9 × 0.9025) ÷ 18] = √0.78745 = 0.88738. d = 1.0 ÷ 0.88738 = 1.1269, a large effect (Lakens: 1.13). J = 1 − 3 ÷ 71 = 68 ÷ 71 = 0.957746, so g = 1.1269 × 0.957746 = 1.0793 (Lakens: 1.08).
The same study from t(18) = 2.52. d = 2.52 × √(1/10 + 1/10) = 2.52 × 0.447214 = 1.1270; g = 1.1270 × 0.957746 = 1.0794. The small gap from 1.1269 comes from t being rounded to 2.52.
Equal SDs, unequal groups. M₁ = 100, M₂ = 105, both SDs 15, n₁ = 30, n₂ = 40. The pooled SD is 15, so d = −5 ÷ 15 = −0.33333, a small effect. J = 1 − 3 ÷ 271 = 268 ÷ 271 = 0.98893, so g = −268 ÷ 813 = −0.32964.
Other questions people ask
How do I calculate effect size?
For two groups, Cohen’s d is the difference in means divided by the pooled standard deviation: d = (M₁ − M₂) ÷ √[((n₁ − 1)SD₁² + (n₂ − 1)SD₂²) ÷ (n₁ + n₂ − 2)]. For means 8.7 and 7.7 with SDs 0.82 and 0.95 and 10 in each group, the pooled SD is 0.887 and d = 1.0 ÷ 0.887 = 1.13.
What is the difference between Cohen’s d and Hedges’ g?
Cohen’s d slightly overstates the effect in small samples. Hedges’ g multiplies d by 1 − 3 ÷ (4(n₁ + n₂) − 9) to remove that bias. With 10 in each group the factor is 68 ÷ 71 = 0.958, so d = 1.13 becomes g = 1.08. With large groups the two are almost equal.
What counts as a small, medium or large effect size?
Cohen’s rough benchmarks for |d| are 0.2 small, 0.5 medium and 0.8 large. Lakens (2013) warns that they are arbitrary: judge an effect against others in your field rather than by the labels alone.
How do I get the effect size from a t-test?
For an independent-samples t-test, d = t × √(1 ÷ n₁ + 1 ÷ n₂). With t(18) = 2.52 and 10 in each group: 2.52 × √0.2 = 1.127. Choose “t statistic” and type t and the two group sizes.
Can the effect size be negative?
Yes. The sign shows which group has the higher mean: d is negative when group 2’s mean is higher. The size label uses |d|, so −0.33 and 0.33 are both small.
Does this work for paired or repeated measures?
No. These formulas are for two independent groups. Paired designs use the standard deviation of the differences or the correlation between the measures, which this page does not take.