# What is the effect size (Cohen’s d)?

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.

- Page: https://www.acalculator.org/statistics/effect-size-calculator
- JSON spec: https://www.acalculator.org/statistics/effect-size-calculator.json
- Version: 754ff8fbeb7d

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | From | Work from the means and standard deviations of the two groups, or from a t statistic. |
| m1 | Mean of group 1 | The mean of group 1. |
| s1 | Standard deviation of group 1 | The standard deviation of group 1, 0 or more. |
| n1 | Size of group 1 | The number of people or observations in group 1, at least 2. |
| m2 | Mean of group 2 | The mean of group 2. |
| s2 | Standard deviation of group 2 | The standard deviation of group 2, 0 or more. |
| n2 | Size of group 2 | The number of people or observations in group 2, at least 2. |
| t | t statistic | The t value of an independent-samples (Student’s) t-test of the two groups. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| d | Cohen’s d | The difference in means divided by the pooled standard deviation. |
| g | Hedges’ g | Cohen’s d × J: corrected for the bias of small samples. |
| size | Size of the effect | Cohen’s label for \|d\|: small from 0.2, medium from 0.5, large from 0.8. |
| j | Correction factor J | 1 − 3 ÷ (4(n₁ + n₂) − 9). |
| diff | Difference in means | Mean of group 1 − mean of group 2. |
| pooled | Pooled standard deviation | √[((n₁ − 1)SD₁² + (n₂ − 1)SD₂²) ÷ (n₁ + n₂ − 2)]. |

## 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)).

## Assumptions

- 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

1. from = means, m1 = 8.7, s1 = 0.82, n1 = 10, m2 = 7.7, s2 = 0.95, n2 = 10 gives d = 1.126908, g = 1.079292, j = 0.957746, pooled = 0.887384, diff = 1, size = 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).
2. from = t, t = 2.52, n1 = 10, n2 = 10 gives d = 1.126978, g = 1.079359, size = 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).
3. from = means, m1 = 100, s1 = 15, n1 = 30, m2 = 105, s2 = 15, n2 = 40 gives d = -0.333333, g = -0.329643, j = 0.98893, pooled = 15, size = 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).

## FAQ

### 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.

## Sources

- 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. Formula 1 (Cohen’s d_s from means and the pooled SD), formula 2 (d_s = t × √(1 ÷ n₁ + 1 ÷ n₂)), formula 4 (Hedges’s g_s = d_s × (1 − 3 ÷ (4(n₁ + n₂) − 9))); movie ratings example, d_s = 1.13 and g_s = 1.08; Cohen’s benchmarks 0.2, 0.5 and 0.8. https://pmc.ncbi.nlm.nih.gov/articles/PMC3840331 (retrieved 2026-10-18)