Effect Size Calculator (Cohen's d)
How big the difference actually is — Cohen's d, Hedges' g and the overlap between two groups, which a p-value never tells you.
Cohen's d is the difference in means divided by the pooled standard deviation, so it is measured in standard deviations and is comparable across studies and units.
How the effect size calculator (cohen's d) works
Cohen's d is the difference in means divided by the pooled standard deviation, so it is measured in standard deviations and is comparable across studies and units.
Hedges' g applies a small-sample correction that removes d's upward bias below about n = 20. The calculator also reports the probability of superiority and the overlap, which are far easier to explain to a non-specialist than "d = 0.5".
Formula: d = (x̄₁ − x̄₂) / sₚ; g = d × (1 − 3/(4(n₁+n₂) − 9))
Worked examples
| Inputs | Cohen's d | Note |
|---|---|---|
| Means 105 and 100, SD 15 | 0.333333 | d = 0.333 — a small effect |
| A medium effect | 0.533333 | d = 0.533 |
| No difference | 0 | d = 0 |
FAQFrequently asked questions
What is Cohen's d?
The difference between two means in units of the pooled standard deviation — a scale-free measure of how big an effect is.
What counts as small, medium and large?
Cohen's rough conventions are 0.2, 0.5 and 0.8. He intended them as a last resort when no field-specific benchmark exists, and they are routinely over-applied.
Why report it alongside a p-value?
Because significance depends on sample size and effect size does not. With 100,000 observations a d of 0.01 is significant and meaningless.
When should I use Hedges' g?
Whenever either group is under about 20. Cohen's d is biased upward in small samples and g corrects it.
What is the probability of superiority?
The chance that a randomly chosen member of group 1 scores above one from group 2. For d = 0.5 it is only 64% — which is a useful corrective to how large "medium" sounds.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.