Effect Size Calculator
An effect size calculator expresses the difference between two groups in standard-deviation units, so results from different scales become comparable. Enter the mean, standard deviation, and sample size for each group to get Cohen's d, the corrected Hedges' g, and their confidence intervals.
Enter the mean, standard deviation, and sample size for each of the two groups. The standardized mean difference is reported as both Cohen's d and the small-sample-corrected Hedges' g.
How to use the effect size calculator
You need three summary numbers from each of the two groups: the mean, the standard deviation, and the sample size. These appear in almost every results table, so you rarely need the raw data.
- 1. Enter the first group. Type its mean, standard deviation, and number of participants.
- 2. Enter the second group. Add the same three numbers for the comparison group.
- 3. Read the standardized mean difference. The calculator pools the two standard deviations, divides the difference in means by that pooled value to give Cohen's d, then applies the small-sample correction to give Hedges' g.
- 4. Note the confidence interval. Each effect size is reported with its interval, so you can see how precisely the difference is estimated.
A worked example
Suppose the treatment group scored a mean of 55 with a standard deviation of 10 across 10 participants, and the control group scored 48 with a standard deviation of 11 across 10 participants. The pooled standard deviation combines the two spreads, weighted by their degrees of freedom, and comes to about 10.5. Cohen's d is the difference in means, 7, divided by that pooled value, giving 0.67.
Because each group has only 10 participants, the small-sample bias is real. Multiplying by the Hedges' correction factor of about 0.96 shrinks the estimate to 0.64. The gap between 0.67 and 0.64 is exactly the upward bias the correction removes, and it is why Hedges' g is the value to report from small studies and the one a meta-analysis pools.
Cohen's d, Hedges' g, and why the correction matters
Cohen's d is the raw standardized mean difference, but it overestimates the true effect when samples are small. Hedges' g multiplies d by a correction factor that depends on the total sample size, pulling the estimate back toward zero; the two values converge as the sample grows. For any study with fewer than about fifty participants per arm, Hedges' g is the figure to report, and it is the standardized mean difference that meta-analysis software pools by default.
If you want the concepts behind the numbers, the explainer on what effect size and Cohen's d really measure covers the benchmarks and the common mistakes. When your outcome is binary rather than continuous, the relevant effect sizes are ratios instead, so reach for the odds ratio calculator or the risk ratio calculator.
To combine standardized mean differences across studies, feed the same summary statistics into the combine them into a pooled estimate and draw the pooled result with the forest plot generator.
Common mistakes to avoid
- Reporting Cohen's d from small samples. With fewer than about fifty participants per arm, Cohen's d runs high. Report the corrected Hedges' g instead, which is what pooling software expects.
- Dividing by the wrong standard deviation. The standardized mean difference uses the pooled standard deviation of both groups, not the standard deviation of one group or the standard error of the mean.
- Treating the benchmarks as rules. The labels small, medium, and large are rough conventions. A small standardized effect can be important for a serious outcome, and a large one can be trivial in a noisy setting.
- Mixing effect sizes from different scales without standardising. The whole point of a standardized mean difference is to make scales comparable. Never pool raw mean differences from instruments that measure on different scales.
Need the effect sizes extracted and pooled correctly?
Pulling means and standard deviations from papers, converting other statistics into a common effect size, and pooling them is where most reviews go wrong. A methodologist can handle the extraction and the analysis end to end.
Get help with your analysisFrequently asked questions
How do I calculate an effect size?
For two groups, the standardized mean difference is the gap between the group means divided by their pooled standard deviation, which gives Cohen's d. This calculator takes the mean, standard deviation, and sample size from each group, computes the pooled standard deviation, and divides the mean difference by it. It then applies the Hedges' g small-sample correction, which shrinks the estimate slightly because Cohen's d is biased upward in small samples, and reports a confidence interval for each.
What does a 0.5 effect size mean?
An effect size of 0.5 means the two group means differ by half of a pooled standard deviation. Using Cohen's widely cited benchmarks, that is a medium effect: large enough to be visible to the naked eye but not overwhelming. Benchmarks are only a rough guide, though, and what counts as meaningful depends on the field and the outcome, so a 0.5 in a tightly controlled lab study and a 0.5 in a noisy real-world trial carry different weight.
Is 0.75 a large effect size?
An effect size of 0.75 sits between Cohen's medium benchmark of 0.5 and his large benchmark of 0.8, so it is usually described as a moderate to large effect. It indicates the groups differ by three-quarters of a standard deviation, which is a substantial separation. As always, the confidence interval matters: a 0.75 with an interval running from 0.2 to 1.3 is far less convincing than the same point estimate with a tight interval, so report the bounds alongside the value.
Can a spreadsheet calculate effect size?
Yes. A spreadsheet can compute the pooled standard deviation and divide the mean difference by it, and you can add the Hedges' correction with a single extra formula. The drawback is that the confidence interval requires the standard error of the standardized mean difference, which is easy to get wrong by hand, and there is no guard against bias in small samples. This calculator handles the pooled standard deviation, the correction, and the interval together so the result matches what a meta-analysis package would produce.
What is the difference between Cohen's d and Hedges' g?
They measure the same thing, a standardized mean difference, but Hedges' g corrects a bias that Cohen's d carries in small samples. Cohen's d tends to overstate the true effect when the total sample is small, so Hedges' g multiplies it by a correction factor that depends on the degrees of freedom. In large samples the factor is almost 1 and the two values are nearly identical; in small samples g is noticeably smaller and is the more accurate figure to report.
Can an effect size be greater than 1?
Yes. A standardized mean difference of more than 1 simply means the two group means are separated by more than one pooled standard deviation, which happens when an intervention has a large effect or the groups are tightly clustered. Values above 1 are common in well-controlled experiments. There is no upper limit, so the size should always be judged against the field and the precision shown by the confidence interval rather than against a fixed ceiling.