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Cohen's d Calculator

Measure the standardized difference between two means.

Result

0.600
Medium

How it is calculated

Cohen's d expresses the gap between two group means in standard deviations: d = (M₁ − M₂) / SD. Here M₁ and M₂ are the two group averages and SD is the standard deviation to scale by, normally the pooled standard deviation of both groups, which you enter yourself. The tool does not compute it from raw data.

SD must be greater than zero. The sign of d shows the direction (positive when M₁ is larger). The label uses the absolute value: under 0.2 negligible, 0.2 to under 0.5 small, 0.5 to under 0.8 medium, 0.8 and above large. These are Cohen's rough rules of thumb, not fixed limits, and what counts as a meaningful effect depends on the field.

Worked example

Group 1 averages 78, group 2 averages 72, and the pooled standard deviation is 10. The difference is 78 − 72 = 6. d = 6 / 10 = 0.600. Since 0.5 ≤ 0.6 < 0.8, the effect is labelled Medium: the groups' means are 0.6 standard deviations apart.

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Common mistakes

  • Dividing by the standard error instead of the standard deviation. That gives a number that grows with sample size and is not an effect size.
  • Entering the standard deviation of one group when the groups differ a lot; the pooled value is what d expects.
  • Treating the small, medium and large labels as a verdict. A d of 0.3 can matter a lot in medicine and little elsewhere.
  • Using d for the difference of means when the data are paired measurements; paired designs use a different standardiser.

About this calculator

This calculator finds Cohen's d, a standardized effect size that measures the difference between two group means in units of standard deviation: d = (M₁ − M₂) / SD_pooled, where the pooled standard deviation combines the variability of both groups. Unlike a raw mean difference or a p-value, d expresses how large a difference is in a scale-free way, regardless of the units the original data were measured in.

Researchers in psychology, medicine, and social science report Cohen's d alongside statistical significance testing to convey practical importance, since a statistically significant result can still reflect a trivially small effect. Jacob Cohen's commonly cited (though context-dependent) benchmarks are around 0.2 for a small effect, 0.5 for medium, and 0.8 for large.

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