Cohen's d Effect Size Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
Cohen's effect size is calculated with d = (mean₁ − mean₂) ÷ pooled standard deviation. A d of 0.63 between two groups is generally interpreted as a medium-to-large effect, according to Cohen's standard scale (0.2 small, 0.5 medium, 0.8 large).
Explanation
A statistical significance test answers a binary question: is the observed difference between two groups probably real, or could it be explained by mere sampling chance? This question, however, says nothing about the practical magnitude of that difference, an important distinction since a very large sample can make a tiny, practically uninteresting difference statistically significant (see our sample size calculator for this link between sample size and statistical power). Cohen's effect size (d) answers this complementary question: it expresses the gap between the two means in units of pooled standard deviation, which makes it independent of the sample size and directly comparable from one study to another, even when the measured variables use different scales. The psychologist Jacob Cohen proposed in 1988 an interpretation scale that has become a widely cited convention in social science and psychology: a d around 0.2 is considered a small effect, around 0.5 a medium effect, and from 0.8 a large effect — useful benchmarks that nonetheless remain general conventions, not rigid universal thresholds, the appropriate interpretation of a given effect size potentially varying by field of study. This calculator uses a simplified version of the formula, suited to groups of equal or similar sizes: the full formula weights the pooled standard deviation by the actual sizes of each group, a nuance that noticeably changes the result only for groups of very different sizes. The standard deviations used as input can be obtained from raw data with our sample variance and standard deviation calculator.
Example: group 1 (mean 75, SD 10) versus group 2 (mean 68, SD 12)
Inputs
Group 1: mean 75, SD 10. Group 2: mean 68, SD 12.
Calculation
Pooled SD = √((10² + 12²) ÷ 2) = √((100+144) ÷ 2) = √122 ≈ 11.045. d = (75 − 68) ÷ 11.045 ≈ 0.6338.
Result
The effect size between these two groups is about 0.63, generally interpreted as a medium-to-large effect on Cohen's scale.
Frequently asked questions
Why isn't a statistically significant result enough to judge the importance of a difference?
Because statistical significance depends heavily on the sample size: with a large enough sample, even a tiny, practically uninteresting difference can become statistically significant. Effect size, on the other hand, measures the real magnitude of the difference independent of the sample size, complementary information essential for judging the practical relevance of a result, not just its statistical reality.
Are Cohen's 0.2 / 0.5 / 0.8 thresholds valid in all fields?
They are general benchmarks proposed by Cohen himself as practical conventions, not rigid universal thresholds applicable without nuance to all research fields. In some fields where measured effects are typically very subtle (certain areas of social psychology, for example), a d of 0.2 can already be considered notable; in other fields, a different threshold may be more relevant depending on the conventions established in that specific field.
Why does the formula used here assume equal group sizes?
This simplified version simply averages the two variances without weighting them by the size of each group, which gives a result identical to the full formula when the two groups have comparable sizes. For groups of very different sizes, the full formula (which weights the pooled standard deviation by each group's degrees of freedom) would give a slightly different result, generally closer to the standard deviation of the larger group.