Quick answer
Cohen's d is the standardised difference between two means: d = (m₁ − m₂) ÷ s_pooled with s_pooled = √(((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2)). Means of 10 and 8 with SD 2 in both groups give d = 1 and a pooled SD of 2.
Enter the mean, SD and size for each group. The calculator returns Cohen's d and the pooled SD. Use this effect size (cohen's d) calculator to check your own figures.
Related tools: Sample Size Calculator: Sample size for estimating a mean or a proportion. Confidence Interval Calculator: Confidence interval for a mean (t or z). Point Estimate Calculator: Point estimates of a proportion (MLE, Laplace and Wilson).
How to use the Effect Size (Cohen's d) Calculator
- Enter mean 1.
- Enter sD 1 (above 0).
- Enter n₁ (a whole number, 2 or more).
- Enter mean 2.
- Enter sD 2 (above 0).
- Enter n₂ (a whole number, 2 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Mean 1 | A number | — |
| SD 1 | A number | > 0 |
| n₁ | A whole number | ≥ 2 |
| Mean 2 | A number | — |
| SD 2 | A number | > 0 |
| n₂ | A whole number | ≥ 2 |
Formula and method
Formula
d = (m₁ − m₂) ÷ s_pooled, s_pooled = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁ + n₂ − 2))
IEEE-754 double precision; shown to at most 6 decimal places.
Pooled-SD standardized mean difference; |d| ≈ 0.2 small, 0.5 medium, 0.8 large (Cohen's conventions).
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Mean 1 = 10; SD 1 = 2; n₁ = 30; Mean 2 = 8; SD 2 = 2; n₂ = 30.
| Result | Value |
|---|---|
| Cohen's d | 1 |
| Pooled SD | 2 |
The first line is the headline result (cohen's d). Below it the effect Size (Cohen's d) Calculator lists pooled SD, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Interpretation
Cohen's rough guide: 0.2 small, 0.5 medium and 0.8 large. A d of 1 means the groups differ by one standard deviation, a large effect: the average person in group 1 scores higher than about 84% of group 2.
Why report it
A p-value says whether an effect exists; the effect size says how big it is, independent of sample size. Each group needs n ≥ 2.
How the result changes with mean 1
Holding every other input at the first worked example, this table changes only mean 1. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Mean 1 | Cohen's d | Pooled SD |
|---|---|---|
| 5 | -1.5 | 2 |
| 10 | 1 | 2 |
| 20 | 6 | 2 |
| 40 | 16 | 2 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- SD 1: entering "0" shows "SD 1 must be greater than 0." beside that field and no result.
Choosing between the Effect Size (Cohen's d) Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Sample Size Calculator](/statistics/sample-size-calculator/) | estimate a, confidence level and margin of error | Required sample size |
| [Confidence Interval Calculator](/statistics/confidence-interval-calculator/) | sample mean, standard deviation and sample size | Confidence interval |
| [Point Estimate Calculator](/statistics/point-estimate/) | successes and trials | Sample proportion |
| [Standard Error Calculator](/statistics/standard-error-calculator/) | statistic, standard deviation or proportion p and sample size | Standard error |
| [Margin of Error Calculator](/statistics/margin-of-error-calculator/) | for a, confidence level and σ or proportion p | Margin of error |
Background: hypothesis testing and inference
A hypothesis test compares a test statistic with what the null hypothesis predicts. The decision rule is to reject the null hypothesis when the p-value is at or below the significance level α, which you should choose before seeing the data (0.05 is conventional, not special). For a two-tailed z test the p-value is 2 × (1 − Φ(|z|)); for a one-sample t test the statistic is (x̄ − μ₀) ÷ (s ÷ √n) with n − 1 degrees of freedom.
Failing to reject the null hypothesis does not prove it true, and a statistically significant result can still be too small to matter in practice.
Assumptions and limitations
- n ≥ 2 per group
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for sD 1 to confirm this.
Frequently asked questions
Is d the same as significance?
No. Effect size says how large a difference is; significance says whether it is unlikely to be chance, and a tiny effect can be significant in a large sample.
What d is large?
By Cohen's convention, d of 0.8 or more is large, 0.5 medium and 0.2 small.
What is Hedges' g?
A small-sample corrected d.
What does the Effect Size (Cohen's d) Calculator calculate?
Cohen's d for two groups. It returns Cohen's d and Pooled SD.
What formula does the Effect Size (Cohen's d) Calculator use?
d = (m₁ − m₂) ÷ s_pooled, s_pooled = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁ + n₂ − 2)). Pooled-SD standardized mean difference; |d| ≈ 0.2 small, 0.5 medium, 0.8 large (Cohen's conventions).
What do I need to enter in the effect Size (Cohen's d) Calculator?
You enter Mean 1, SD 1, n₁, Mean 2, SD 2 and n₂.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. n ≥ 2 per group.
What is an example of a effect Size (Cohen's d) result?
With mean 1 10, sD 1 2, n₁ 30, mean 2 8 and sD 2 2, the cohen's d is 1.
Where does the method come from?
The method follows: Cohen J, Statistical Power Analysis for the Behavioral Sciences, 2nd ed. (1988).
Related calculators
- Sample Size Calculator — Sample size for estimating a mean or a proportion.
- Confidence Interval Calculator — Confidence interval for a mean (t or z).
- Point Estimate Calculator — Point estimates of a proportion (MLE, Laplace and Wilson).
- Standard Error Calculator — Standard error of a mean or a proportion.
- Margin of Error Calculator — Margin of error for a mean or a proportion.
- Odds Ratio Calculator — Odds ratio from a 2×2 table.
Sources
- Cohen J, Statistical Power Analysis for the Behavioral Sciences, 2nd ed. (1988)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.