Cohen’s d Calculator

What this calculator does

Cohen d expresses the difference between two means in pooled standard deviations. Means of 85 and 78 with a pooled standard deviation of 13.003 give d = 0.5383, conventionally described as a medium effect.

Its value is that it is unaffected by sample size, which p-values are not. A trivial difference becomes statistically significant with enough data, but its effect size stays trivial. Reporting both is the only way to distinguish a result that is detectable from one that matters.

The formula

Formulad = (x̄₁ − x̄₂) / sp; sp = √[((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)]

The difference between the two means is divided by the pooled standard deviation, which weights each sample variance by its degrees of freedom. The conventional labels are 0.2 for small, 0.5 for medium and 0.8 for large, though Cohen himself described these as arbitrary and intended only for fields with no better benchmarks.

Term	Meaning
Cohen’s d	The mean difference in pooled standard deviations.
Pooled standard deviation	The combined spread estimate weighted by degrees of freedom.
Effect size	A measure of magnitude that does not depend on sample size.
Hedges’ g	A version corrected for small-sample bias, preferable below about 20 per group.

The inputs explained

Field	What to enter
Group 1 mean	Group 1 mean.
Group 1 standard deviation	Group 1 standard deviation.
Group 1 size	Group 1 size.
Group 2 mean	Group 2 mean.
Group 2 standard deviation	Group 2 standard deviation.
Group 2 size	Group 2 size.

When to use it

Reporting a trial result

Journals increasingly require an effect size alongside any p-value, since significance alone does not convey magnitude.

Planning a study

Power calculations need an expected effect size, usually taken from previous work in the field.

Comparing across studies

Because it is scale-free, d allows results measured on different instruments to be compared, which is the basis of meta-analysis.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How does the mean difference map to d?

A range of group 1 means against the same comparison group.

Group 2 fixed at 78, pooled SD 13.003

Group 1 mean	Cohen's d	Magnitude	Mean difference
80	0.1538	Negligible	2.000
82	0.3076	Small	4.000
85	0.5383	Medium	7.000
90	0.9229	Large	12.000

The pooled standard deviation stays at 13.003 throughout, so d is simply the mean difference divided by it. A 2-point gap is negligible at 0.1538, a 7-point gap is medium at 0.5383 and a 12-point gap is large at 0.9229. Note that none of this depends on the sample size, which is the whole point of an effect size.

Questions

What counts as a large effect?

The conventional labels are 0.2 small, 0.5 medium and 0.8 large, but Cohen offered them only as a fallback for fields lacking their own benchmarks and described them as arbitrary. In a well-studied area, compare against typical effects in that literature instead.

Why report an effect size as well as a p-value?

Because a p-value depends on sample size and an effect size does not. With 100,000 observations a difference of no practical consequence will be highly significant. The effect size is what tells you whether the difference is worth anything.

What is the difference between Cohen’s d and Hedges’ g?

Hedges g applies a small-sample correction that reduces the slight upward bias in d. The two are nearly identical above about 20 per group, and g is the better choice below that. Some software reports g while still calling it d.

Can d be negative?

Yes, and the sign simply indicates which group is larger. The magnitude is what matters, so effect sizes are usually reported as absolute values with the direction described separately in words.

For the denominator, see the pooled standard deviation calculator. For the sample size it implies, see the power analysis calculator.

Cohen's d (effect size) calculator