Enter the means and standard deviations for two groups to calculate Cohen's d effect size. You can also calculate using t-value and degrees of freedom. Results include the Cohen's d value, effect-size correlation r, and an interpretation of effect magnitude (small, medium, or large).
Cohen's d
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Effect-Size Correlation (r)
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Pooled Standard Deviation
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Effect Magnitude
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Cohen's d is a standardized measure of the difference between two group means, expressed in units of standard deviation. It tells you how large a difference is in practical terms, independent of sample size. A d of 0.5 means the groups differ by half a standard deviation.
Cohen's d = (M1 − M2) / s_pooled, where the pooled standard deviation is s_pooled = √[(s1² + s2²) / 2]. This formula assumes roughly equal group sizes and homogeneous variance.
When you have results from an independent-samples t-test, you can use Cohen's d = 2t / √(df), where t is the t-statistic and df is the degrees of freedom. This is useful when you have published t-test results but not the raw means and SDs.
Cohen (1988) proposed the following conventional benchmarks: a d of 0.2 is considered small, 0.5 is medium, and 0.8 or above is large. These are guidelines only — the meaningfulness of an effect always depends on the research context.
The effect-size correlation r (also written r_Yl) converts Cohen's d into a Pearson correlation-like measure. It is calculated as r = d / √(d² + 4). Like d, it quantifies effect magnitude on a scale that many find more intuitive, ranging from 0 to 1.
The classic pooled-SD formula assumes the two groups have similar variances. If the variances are very different (heterogeneous), Glass's Δ — which uses only the control group's SD — may be more appropriate. For equal SDs the two measures agree.
Yes. Cohen's d is negative when M2 is larger than M1. The sign reflects the direction of the difference. Many researchers report the absolute value and describe direction in words, but retaining the sign is useful when the direction of the effect was predicted in advance.
Cohen's d measures effect size for differences between means (continuous outcomes), while Cohen's h measures effect size for differences between two proportions (binary outcomes). Use Cohen's h when comparing percentages or probabilities; use Cohen's d for continuous measures like test scores or reaction times.