Effect Size Calculator
Enter the mean, standard deviation and sample size for two groups. The calculator gives Cohen's d, the small-sample corrected Hedges' g and plain-language measures of how far apart the groups really are.
- Cohen's d and Hedges' g
- Overlap and superiority
- Correlation r
Uses the pooled standard deviation. Group 1 minus group 2, so a positive d means group 1 scored higher.
A p-value says whether there is a difference. Effect size says how big it is. With a large enough sample, even a tiny difference becomes statistically significant. Effect size puts the difference in standard deviation units, so you can compare studies and judge whether the result matters in practice.
Interpreting effect sizes
Cohen's benchmarks and what they mean. Search for a value or label.
| d | Label | Overlap | Probability of superiority | n per group (80% power) |
|---|---|---|---|---|
| 0.1 | Negligible | 96% | 53% | 1571 |
| 0.2 | Small | 92% | 56% | 393 |
| 0.3 | Small | 88% | 58% | 175 |
| 0.5 | Medium | 80% | 64% | 63 |
| 0.8 | Large | 69% | 71% | 25 |
| 1 | Large | 62% | 76% | 16 |
| 1.2 | Very large | 55% | 80% | 11 |
| 2 | Huge | 32% | 92% | 4 |
Cohen offered these as rough guides when nothing better is known. In education, a d of 0.4 is often a meaningful result. In medicine, small effects on serious outcomes can matter a lot.
What a value of d looks like
Overlap, superiority and the sample you would need. Slide d from tiny to huge.
Even a large effect of 0.8 leaves two thirds of the groups overlapping. Effects in real data are rarely as clean as the labels suggest.
How Cohen's d is calculated
Difference divided by spread. Step through it with the example values.
Take the difference
78 − 72 = 6 points.
Hedges' g multiplies d by a correction factor, J = 1 − 3 ÷ (4(n1 + n2) − 9). With 40 per group it changes d by about 1%.
d, g or r
Three ways to report the same effect. Pick a measure.
The standard measure for comparing two means. Slightly overstates the effect in small samples.
d with a small-sample correction. Preferred in meta-analysis.
Expresses the same difference as a correlation between group and score.
Many journals ask for an effect size with a confidence interval. Report the one used in your field, and give the means and SDs so others can convert.
Reporting an effect size
Make it easy to interpret. Tick each item.
Tick each item as you go.
A confidence interval around d shows how precise your estimate is. With small samples it can easily span from no effect to a large one.
What the calculator reports
Standard and plain-language measures. Each tile explains one result.
Mean difference in pooled SD units.
d corrected for small samples.
Share of the two distributions that overlap.
Chance a random group 1 member beats group 2.
The same effect as a correlation.
Probability of superiority is often the easiest to explain. A value of 64% means a random person from group 1 scores higher than a random person from group 2 nearly two times in three.
Frequently Asked Questions
No question matches that search.
What is a good effect size?
It depends on the field. Cohen's guide calls 0.2 small, 0.5 medium and 0.8 large, but a small effect on an important outcome can matter more than a large effect on a trivial one.
How do I calculate Cohen's d?
Subtract one mean from the other and divide by the pooled standard deviation of the two groups.
What is the difference between Cohen's d and Hedges' g?
Hedges' g applies a small correction for sample size. They are almost identical above 20 per group.
Can effect size be negative?
Yes. The sign shows which group is higher. The size is what matters for interpretation.
How many participants do I need to detect a medium effect?
About 64 per group for d = 0.5 at 80% power and α = 0.05.
How do I convert d to r?
r = d ÷ √(d² + (n1 + n2)² ÷ (n1 × n2)). With equal groups that is close to d ÷ √(d² + 4).
Is effect size the same as statistical significance?
No. Significance depends on sample size; effect size does not.
Report how big, not just whether
Enter the means, SDs and sample sizes, report d or g with the direction and add a plain-language measure such as probability of superiority. Readers can then judge whether your result matters, not just whether it passed a significance test.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.