This Cohen’s d calculator measures effect size — how big a difference between two groups actually is, in standard-deviation units — from the two means and standard deviations, with the pooled SD and interpretation benchmarks.
Without n’s, the pooled SD uses the simple average of variances (the equal-n formula). With n’s entered, it uses the degrees-of-freedom-weighted version. Either way, d answers “how much?” — the question p-values cannot.
"Significant" Is Not "Big"
A p-value fuses effect size with sample size; d separates them: d = (mean₁ − mean₂) ÷ pooled SD. A d of 0.9 means the groups' centers sit nearly a full standard deviation apart — visible to the naked eye on overlapping histograms — whether it came from 20 subjects or 20,000. Cohen's conventions (0.2 small, 0.5 medium, 0.8 large) are starting points for judgment, best calibrated against effects you know in the same field (a d = 0.3 drug effect can be a blockbuster; a d = 0.3 tutoring effect can be mediocre). Part of our Statistics Calculators collection.
Worked Example (Verified)
Group 1: mean 80, SD 10 · Group 2: mean 70, SD 12 (the widget's defaults):
- Pooled SD = √((100 + 144) ÷ 2) = √122 = 11.05
- d = (80 − 70) ÷ 11.05 = 0.905 — a large effect by the conventions
- Human translation: the average Group-1 member scores higher than ~82% of Group 2 (that's Φ(0.905)); a random Group-1 member beats a random Group-2 member about 74% of paired draws — real separation, honest overlap
- The same 10-point gap with SDs of 40 would be d = 0.25 — small; raw differences mean nothing until spread prices them, which is the entire point
Fine Print
- Hedges' g applies a small-sample correction (multiply d by ~1 − 3/(4(n₁+n₂) − 9)) — meta-analyses prefer it; below n ≈ 20 per group, d overstates slightly.
- Glass's Δ uses only the control group's SD — the right choice when the treatment itself changes spread.
- d assumes roughly normal, similar-shaped distributions; for skewed outcomes, rank-based effect sizes (or a transformed scale) tell a truer story.
- Report d with its confidence interval in real work — an effect size is still an estimate.
Related Tools
- P-Value Calculator — significance, the other half of the report
- Standard Deviation Calculator — the SDs feeding the pool
- Statistics Calculators — the full collection
Frequently Asked Questions
How do you calculate Cohen's d?
Divide the mean difference by the pooled standard deviation: d = (M₁ − M₂) / SD_pooled, with SD_pooled = √[(SD₁² + SD₂²)/2] for equal groups (or the df-weighted version with your n's). Example: (80 − 70) / 11.05 = 0.905.
What is a good Cohen's d?
Cohen's landmarks: 0.2 small, 0.5 medium, 0.8 large — conventions, not laws. Judge within your field's distribution of real effects: education interventions cluster at 0.1–0.3; height differences between sexes reach d ≈ 1.7. "Good" is comparative.
What is the difference between d and a p-value?
p answers "could chance produce a gap at least this wide, at this n?" d answers "how wide is the gap, in spread units?" — sample size moves p enormously and d not at all (in expectation). Serious reports give both.
Can Cohen's d exceed 1?
Freely — it is not a correlation and isn't bounded by 1. d = 2 means two SDs apart (groups barely overlap, ~2.3% shared area extremes); textbook psychology rarely sees it, physics-grade interventions and sex differences in height do.
What does the sign of d mean?
Direction only: positive means Group 1's mean is higher, by the order you entered them. Magnitudes are compared as |d|. Publications define the direction explicitly ("positive favors treatment") and stick to it.
Is this Cohen's d calculator free?
Yes — free, instant, no sign-up.