Home › Statistics & Probability Calculators › Cohen's d Calculator (Effect Size)
Cohen's d Calculator (Effect Size)
Cohen’s d expresses the difference between two group means in standard-deviation units, so results measured on different scales can be compared. Enter each group’s mean, standard deviation and size. The calculator pools the two standard deviations, divides the mean difference by the pooled value and reports the small-sample corrected version, Hedges’ g.
Cohen’s rough benchmarks are 0.2 for a small effect, 0.5 for medium and 0.8 for large, but what counts as important depends on the field. A d of 0.5 means the average member of group 1 scores half a standard deviation above the average member of group 2. Under a normal model that places them at about the 69th percentile of group 2 (Cohen’s U₃, shown below the result).
The confidence interval uses the usual large-sample standard error of d. Glass’s Δ, which divides by the second (control) group’s standard deviation only, is included for studies where the treatment changes the spread. To test whether the difference is significant, run the two-sample t-test; d and t are linked by t = d ÷ √(1/n₁ + 1/n₂).
Result and step-by-step solution
A medium effect by Cohen’s benchmarks (0.2 small, 0.5 medium, 0.8 large). Hedges’ g = 0.6311.
- Pooled standard deviationsp = √{[(n₁ − 1)s₁² + (n₂ − 1)s₂²] ÷ (n₁ + n₂ − 2)} = √{[29 × 9.2² + 27 × 10.5²] ÷ 56} = 9.8482
- Cohen’s dd = (x̄₁ − x̄₂) ÷ sp = (78.4 − 72.1) ÷ 9.8482 = 0.6397
- Small-sample correction (Hedges’ g)J = 1 − 3 ÷ (4 × df − 1) = 1 − 3 ÷ (4 × 56 − 1) = 0.98655; g = d × J = 0.6311
- Confidence interval for dSE(d) = √[(n₁ + n₂)/(n₁n₂) + d²/(2(n₁ + n₂))] = 0.2694; 95% CI = 0.1117 to 1.1677 (normal approximation)
| Glass’s Δ (uses group 2 SD) | 0.6 |
|---|---|
| d using the average of the two variances | 0.6382 |
| Distribution overlap (normal model) | 74.9% |
| Cohen’s U₃ (share of group 2 below the group 1 mean) | 73.9% |
Frequently asked questions
- How do you calculate Cohen's d?
- Subtract one mean from the other and divide by the pooled standard deviation, sp = √{[(n₁ − 1)s₁² + (n₂ − 1)s₂²] ÷ (n₁ + n₂ − 2)}.
- What is a good Cohen's d?
- By Cohen’s conventions 0.2 is small, 0.5 medium and 0.8 large. In education research, effects of 0.2 to 0.4 are often considered meaningful.
- What is the difference between Cohen's d and Hedges' g?
- Hedges’ g multiplies d by a correction factor J = 1 − 3/(4df − 1) that removes the slight upward bias of d in small samples. With 20+ per group they are nearly identical.
- Can Cohen's d be negative?
- Yes. The sign only shows which group has the larger mean. Report the absolute value with a note of the direction.
Last reviewed: October 7, 2026. Calculations run in your browser and were validated against SciPy.