Effect Size Calculator (Cohen's d)

Effect size is a measure of the practical magnitude of a difference or relationship, separate from whether that difference is statistically significant. A study with a very large sample can detect even a trivially small difference as statistically significant, so reporting effect size alongside a p-value gives readers a much clearer picture of what the result actually means in practice. The most widely used effect size for comparing two group means is Cohen's d, which expresses the difference in means as a multiple of the pooled standard deviation. A d of 0.2 is conventionally small, 0.5 is medium, and 0.8 or above is large. A d of 1.0 means the two group means are one standard deviation apart, which represents a very large and practically meaningful difference in most applied fields. For analysis of variance (ANOVA) results, the equivalent measure is eta squared, which expresses the proportion of total variance explained by the factor: values below 0.01 are small, 0.06 is medium, and 0.14 or above is large. This calculator has two modes. In the first mode, enter the mean of each group and the pooled standard deviation to get Cohen's d. In the second mode, enter the F-statistic and the degrees of freedom to get eta squared. Both modes show the numerical result and the conventional interpretation. Results are for educational and research planning purposes.

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1.00
Cohen's d
InterpretationLarge
Absolute d1.00
Mean difference5.00
Overlap %61.7%

Cohen's d: small < 0.2, medium 0.2-0.8, large > 0.8. Eta squared: small < 0.01, medium 0.01-0.14, large > 0.14. These are general guidelines only.

How it works

Cohen's d = (Mean1 - Mean2) / Pooled SD. The pooled SD should be calculated as the square root of the weighted average of the two group variances. The percentage overlap between two normal distributions with a given d is approximately 2 × Φ(-|d|/2) × 100, where Φ is the standard normal CDF. Smaller overlap means a more distinct separation between groups.

Eta squared = (F × df_between) / (F × df_between + df_within). This gives the proportion of variance explained by the factor in an ANOVA.

Worked example

Group 1 mean = 75, Group 2 mean = 70, pooled SD = 5. Cohen's d = (75 - 70) / 5 = 1.00. This is a large effect: the two group means are exactly one standard deviation apart. The approximate overlap between the two distributions is about 62 percent (61.7%), meaning there is still substantial overlap even with a large effect size. These match the defaults pre-filled in the calculator above.

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Frequently asked questions

What is Cohen's d?

Cohen's d is the standardised difference between two group means, calculated as (mean1 minus mean2) divided by the pooled standard deviation. It expresses the difference in units of standard deviations. By convention: d less than 0.2 is negligible, 0.2 to 0.5 is small, 0.5 to 0.8 is medium, and above 0.8 is large. A d of 1.0 means the means are one standard deviation apart.

What is eta squared in statistics?

Eta squared is the proportion of total variance explained by a factor in ANOVA. It is calculated as F times df_between divided by (F times df_between plus df_within). By convention: eta squared less than 0.01 is small, 0.01 to 0.06 is medium, and above 0.14 is large. It is analogous to R squared in regression.

What is the difference between statistical significance and effect size?

Statistical significance (a p-value) tells you whether an observed difference is likely due to chance. Effect size tells you how large or practically meaningful the difference is. A very large sample can make a tiny, practically irrelevant difference statistically significant. Reporting effect size alongside p-values gives a fuller picture of the result.