Cohen's d Calculator — Effect Size
Enter the means, standard deviations and sample sizes for two groups to get Cohen's d (standardised mean difference), Hedges' g (bias-corrected) and the probability of superiority.
Standardised mean difference — positive means group 1 scored higher
- 1
Mean difference
50 − 45 = 5 - 2
Pooled variance
((30 − 1) × 10² + (30 − 1) × 12²) ÷ (30 + 30 − 2) = 122Weighted average of both group variances. - 3
Pooled SD
√122 = 11.0454 - 4
Cohen's d
5 ÷ 11.0454 = 0.4527
How does this calculator work?
Cohen's d = (mean₁ − mean₂) / pooled SD, where pooled SD = √[((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)]. Values < 0.2 are negligible, 0.2–0.5 small, 0.5–0.8 medium, ≥ 0.8 large. For small samples prefer Hedges' g (= d × bias-correction factor). The probability of superiority ≈ Φ(|d|/√2) translates d into a win-rate.
Formula
How this is calculated
Cohen's d is the most widely used standardised effect size for comparing two group means. Dividing the raw mean difference by the pooled standard deviation expresses the separation in units of spread rather than the original measurement scale, so studies using different scales can be compared directly. Cohen proposed conventional labels: |d| < 0.2 = negligible, 0.2–0.5 = small, 0.5–0.8 = medium, ≥ 0.8 = large, though these thresholds are field-dependent.
The pooled standard deviation is the root of the weighted average of the two group variances: SD_pooled = √[((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)]. This gives more weight to the larger group. Hedges' g applies a small-sample bias correction: g = d × (1 − 3/(4(n₁+n₂)−9)), which brings the estimate closer to the population value when total sample size is below about 20. Glass's Δ uses only the control (group 2) SD as denominator — preferred when the treatment is expected to affect the variance.
The probability of superiority (P(X₁ > X₂) ≈ Φ(|d|/√2)) is a useful plain-language complement: a d of 0.5 means a randomly chosen person from group 1 scores higher than a randomly chosen person from group 2 about 64% of the time. This assumes both groups are approximately normally distributed and the effect is consistent across individuals.
Frequently asked questions
Always prefer Hedges' g when your combined sample size (n₁+n₂) is below about 50. Cohen's d is a biased estimator for small samples — it systematically overstates the effect size — and Hedges' g applies a correction factor that shrinks d toward its true value. For n > 50 the difference is negligible.
A d of 0.5 (medium effect) means the group 1 mean sits at the 69th percentile of group 2's distribution, and a randomly chosen group 1 member scores higher than a randomly chosen group 2 member about 64% of the time. Many real-world educational and clinical interventions produce d values between 0.2 and 0.8.
No — Cohen himself cautioned they are only rough guides. What counts as a large effect in pharmacology (where d > 0.8 is rare) is different from psychology or education (where larger effects are more common). Always interpret d relative to the norms of your field and the practical importance of the difference.
Also known as
TG we-Calculate Editorial Team. (2026). Cohen's d Calculator — Effect Size [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cohens-d-calculator
TG we-Calculate Editorial Team. "Cohen's d Calculator — Effect Size." TG we-Calculate. 2026. https://we-calculate.com/calculator/cohens-d-calculator.
TG we-Calculate Editorial Team, "Cohen's d Calculator — Effect Size," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cohens-d-calculator
@misc{wecalculate_cohens_d_calculator, title = {Cohen's d Calculator — Effect Size}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cohens-d-calculator}}, year = {2026}, note = {TG we-Calculate} }
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