Effect Size Calculator (Cohen's d). Calculate Cohen's d effect size between two groups using their means and standard deviations. Enter Mean 1, SD 1, Mean 2, and SD 2 — and you'll get back Cohen's d, the effect-size correlation r, and an interpretation (small, medium, or large). You can also calculate using t-value and degrees of freedom from an independent groups t-test. Also try the P-Value Calculator.
Cohen's d is a standardized measure of the difference between two group means, expressed in units of the pooled standard deviation. It tells you how large the difference is, independent of sample size. A d of 0 means no difference, while larger values indicate stronger effects. See also our Regression Equation — Least Squares Regression.
Cohen's d = (M1 − M2) / s_pooled, where s_pooled = √[(SD1² + SD2²) / 2]. The pooled standard deviation combines the variability of both groups, giving a common scale for comparison.
Jacob Cohen (1988) proposed that d = 0.2 is a small effect, d = 0.5 is a medium effect, and d = 0.8 is a large effect. These are rough guidelines — what counts as meaningful depends on your field and research context.
The effect-size correlation r (also called r_YL) is another way to express effect magnitude on a −1 to +1 scale, similar to a Pearson correlation. It's calculated as r = d / √(d² + 4). Values of 0.1, 0.3, and 0.5 correspond roughly to small, medium, and large effects.
If you ran an independent-samples t-test, you can compute Cohen's d as d = 2t / √(df), where t is your t-statistic and df is the degrees of freedom. The corresponding r is calculated as r = √(t² / (t² + df)).
Unlike p-values, Cohen's d is not directly influenced by sample size — it measures the magnitude of the difference, not its statistical significance. However, with small samples the estimate of d can be unstable. A correction (Hedges' g) applies a small-sample bias adjustment.
Cohen's d is appropriate when comparing the means of two groups on a continuous outcome. For correlational analyses, use Pearson's r. For categorical outcomes or contingency tables, consider Cramér's V or phi. For ANOVA, eta-squared or omega-squared are more appropriate.
Yes. If the mean of Group 2 is larger than Group 1, Cohen's d will be negative. The absolute value of d represents the magnitude, while the sign indicates direction. Many researchers report the absolute value and specify the direction separately. You might also find our calculate Standard Deviation Index Standard Deviation Index (SDI) useful.