Cohen's d Effect Size Calculator
Calculate Cohen's d — the standardized difference between two group means in pooled standard deviation units. Measures how big an effect is, not just whether it is significant.
Last updated: May 2026
Compare with similar
About this calculator
Cohen's d is a standardized measure of effect size — it expresses the difference between two group means in units of pooled standard deviation, answering not just whether two groups differ but by how much in practical terms. The formula is d = (mean₁ − mean₂) / pooled standard deviation, and this calculator computes the pooled standard deviation as √((SD₁² + SD₂²) / 2), the root-mean-square of the two groups' standard deviations (appropriate when group sizes are similar). The result is a unitless number: a d of 1.0 means the two means differ by one full standard deviation. Effect size is a vital complement to statistical significance (the p-value), because significance tells you whether an effect is likely real but says nothing about whether it is large enough to matter. A trivial difference can be highly significant with a large enough sample, while a meaningful difference can fail significance in a small one. Jacob Cohen proposed rough benchmarks: d ≈ 0.2 is a small effect, 0.5 medium, and 0.8 large, though these are conventions, not laws, and what counts as meaningful depends on the field. Cohen's d underpins meta-analysis (which combines effect sizes across studies) and power analysis (which uses an expected effect size to determine the sample size needed). Edge cases and cautions: the sign of d reflects which mean is larger and is often reported as an absolute value; for unequal group sizes a weighted pooled SD (using degrees of freedom) is more accurate, and for small samples a bias-corrected version called Hedges' g is preferred. Cohen's d assumes roughly normal distributions with comparable variances.
How to use
Example 1 — Group 1 mean 105, Group 2 mean 100, both SDs 15. Enter Group 1 Mean = 105, Group 2 Mean = 100, SD1 = 15, SD2 = 15. Pooled SD = √((225 + 225)/2) = √225 = 15, so d = (105 − 100) / 15 = 0.33. Verify: a difference of one-third of a standard deviation is a small-to-medium effect by Cohen's benchmarks. Example 2 — means 110 and 100 with SDs 18 and 22. Enter 110, 100, 18, 22. Pooled SD = √((324 + 484)/2) = √404 ≈ 20.1, so d = 10 / 20.1 ≈ 0.50. Verify: a d of about 0.5 is a medium effect — the groups differ by roughly half a standard deviation, a difference likely to be visible in practice.
Frequently asked questions
What is the difference between effect size and statistical significance?
Statistical significance (the p-value) tells you whether an observed difference is likely real rather than due to chance, while effect size (Cohen's d) tells you how large that difference is in practical terms. They answer different questions, and you need both. With a very large sample, even a trivially small difference can be statistically significant yet practically meaningless; conversely, a genuinely important difference can fail to reach significance in a small study. Reporting only the p-value is a widespread mistake that obscures whether a result actually matters. Cohen's d puts the magnitude of the effect front and center, which is why journals increasingly require effect sizes alongside p-values.
How do I interpret the value of Cohen's d?
Jacob Cohen offered rough benchmarks: a d around 0.2 is a small effect, 0.5 is medium, and 0.8 or above is large, with values above 1.0 representing very large differences. A d of 1.0 means the two group means differ by a full standard deviation. However, these thresholds are conventions, not strict rules, and the practical importance of a given effect size depends heavily on the field and context — a small d can be hugely important in medicine, while a large d might be unremarkable elsewhere. The sign simply indicates which group's mean is higher and is often reported as an absolute value. Always interpret d relative to your domain rather than mechanically applying the labels.
When should I use Hedges' g instead of Cohen's d?
Hedges' g is a bias-corrected version of Cohen's d that you should prefer when sample sizes are small (roughly under 20 per group), because Cohen's d slightly overestimates the true effect size in small samples. Hedges' g applies a correction factor that shrinks the estimate to remove this upward bias, giving a more accurate value. For large samples the two are nearly identical, so the choice matters most for small studies and meta-analyses combining them. Many statistical packages report g by default for this reason. If you have small or unequal groups, look for Hedges' g or a pooled standard deviation weighted by degrees of freedom rather than the simple version used here.
What is a common mistake when calculating Cohen's d?
A frequent error is using the standard deviation of just one group, or the standard error instead of the standard deviation, rather than the pooled standard deviation of both groups — this distorts the result. Another is applying the simple root-mean-square pooling used here when group sizes are very unequal, where a degrees-of-freedom-weighted pooled SD is more appropriate. People also misread the benchmarks as hard rules, or report d without context about what magnitude is meaningful in their field. Finally, ignoring the assumptions of roughly normal distributions and comparable variances can make d misleading. Use the correct pooled SD, check your assumptions, and interpret the result in domain context.
When should I NOT use this calculator?
Avoid it when your two groups have very different sizes, since the simple pooled standard deviation used here assumes comparable group sizes — use a degrees-of-freedom-weighted pooled SD instead. For small samples, prefer the bias-corrected Hedges' g rather than Cohen's d. It is also inappropriate when the data are far from normally distributed or when the groups have very different variances, which violate the measure's assumptions; nonparametric effect sizes may suit better. Do not use Cohen's d for comparing more than two groups (consider eta-squared or omega-squared) or for correlational data (use r). And remember effect size complements, not replaces, significance testing and confidence intervals. Use it for the standardized difference between two roughly normal groups of similar size.