# Cohen's D Calculator

Free Cohen's d calculator. Calculate the standardized effect size between two groups, plus Hedges' g, distribution overlap, and probability of superiority.

## What this calculates

Calculate Cohen's d to measure the practical significance of the difference between two group means. Also computes Hedges' g (bias-corrected), distribution overlap, and the common language effect size.

## Inputs

- **Group 1 Mean** — Mean of the first group (e.g., treatment group).
- **Group 2 Mean** — Mean of the second group (e.g., control group).
- **Group 1 Standard Deviation** — min 0.0001 — Standard deviation of the first group.
- **Group 2 Standard Deviation** — min 0.0001 — Standard deviation of the second group.
- **Group 1 Size (n1)** — min 2 — Number of observations in group 1.
- **Group 2 Size (n2)** — min 2 — Number of observations in group 2.

## Outputs

- **Cohen's d** — The standardized mean difference (effect size).
- **|Cohen's d|** — Absolute value of Cohen's d.
- **Effect Size** — formatted as text — Interpretation based on Cohen's benchmarks.
- **Pooled Standard Deviation** — The pooled SD used in the denominator.
- **Hedges' g (bias-corrected)** — Cohen's d with small-sample correction factor.
- **Distribution Overlap (%)** — Approximate percentage overlap between the two distributions.
- **CLES (Probability of Superiority)** — Probability that a random value from Group 1 exceeds one from Group 2.
- **Formula** — formatted as text — Step-by-step calculation.

## Details

Cohen's d is the most widely used measure of effect size for comparing two groups. It expresses the difference between group means in standard deviation units.

**The Formula:**

d = (M1 - M2) / s_pooled

where s_pooled = sqrt[((n1-1)s1^2 + (n2-1)s2^2) / (n1+n2-2)]

**Cohen's Benchmarks:**

| |d| Value | Interpretation |
|-----------|----------------|
| < 0.2     | Negligible     |
| 0.2       | Small          |
| 0.5       | Medium         |
| 0.8       | Large          |

**Hedges' g** corrects Cohen's d for small-sample upward bias using the factor J = 1 - 3/(4*df - 1). For samples of 20+ per group, the difference is small.

**Common Language Effect Size (CLES):** This translates d into a probability. If d = 0.5, there is about a 64% chance that a randomly selected person from Group 1 scores higher than a randomly selected person from Group 2.

**Distribution Overlap:** Shows how much the two bell curves overlap. Even a "large" effect (d = 0.8) still has about 69% overlap, which is why individual predictions from group differences are unreliable.

## Frequently Asked Questions

**Q: What is the difference between Cohen's d and Hedges' g?**

A: Both measure standardized mean differences. Cohen's d has a slight upward bias in small samples. Hedges' g multiplies d by a correction factor (approximately 1 - 3/(4n-9)) to remove that bias. For large samples (n > 20 per group), the two are nearly identical. Use Hedges' g when sample sizes are small or when reporting in a meta-analysis.

**Q: Why should I report effect size alongside p-values?**

A: P-values depend on sample size. A very large sample can produce a tiny p-value for a trivial difference. Effect size is independent of sample size and tells you how large the difference actually is. The American Psychological Association and many journals now require effect sizes in addition to p-values.

**Q: What is the Common Language Effect Size (CLES)?**

A: CLES converts Cohen's d into an intuitive probability: the chance that a random person from Group 1 scores higher than a random person from Group 2. A d of 0 gives CLES = 50% (coin flip). A d of 0.8 gives CLES of about 71%. It is often the easiest effect size measure for non-statisticians to understand.

**Q: Can Cohen's d be greater than 1?**

A: Yes. Cohen's d has no upper limit. A d of 2.0 means the two group means are 2 pooled standard deviations apart, which is a very large separation. In education research, effect sizes above 1.0 are common for intensive interventions. In medical research, values above 1.0 typically indicate a strong treatment effect.

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Source: https://vastcalc.com/calculators/statistics/cohens-d
Category: Statistics
Last updated: 2026-04-08