Math
Pooled sample standard deviation
Combine two sample standard deviations using their degrees of freedom as weights to estimate the shared within-group standard deviation.
Calculators / Math / Cohen’s d for independent groups
Cohen’s d for independent groups calculator
Express a difference between independent sample means in pooled standard-deviation units.
On this page
Cohen’s d1
Pooled standard deviation10
Calculator controls
How to calculate
Express a difference between independent sample means in pooled standard-deviation units.
Cohen’s d =
(m1-m2)/(sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)))Pooled standard deviation =
sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2))Worked example
- First sample mean: 80
- Second sample mean: 70
- First sample standard deviation: 10
- Second sample standard deviation: 10
- First sample size: 20
- Second sample size: 20
- Cohen’s d: 1
- Pooled standard deviation: 10
Assumptions and limits
Uses the pooled sample standard deviation and assumes comparable variances. It does not compute significance, causal impact or a small-sample bias correction.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Express a difference between independent sample means in pooled standard-deviation units. The sign follows first mean minus second mean. Interpreting magnitude requires context rather than universal effect labels.
When this tool is useful
The sign follows first mean minus second mean. Interpreting magnitude requires context rather than universal effect labels.
Understanding your inputs
| Input | Example |
|---|---|
First sample mean m1 | 80 |
Second sample mean m2 | 70 |
First sample standard deviation s1 | 10 |
Second sample standard deviation s2 | 10 |
First sample size n1 | 20 |
Second sample size n2 | 20 |
Frequently asked questions
Which assumptions matter for this result?
Uses the pooled sample standard deviation and assumes comparable variances. It does not compute significance, causal impact or a small-sample bias correction.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.