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Effect size calculator — Cohen's d, Hedges' g, r

Enter the mean, SD and n of two groups to get the standardized mean difference — Cohen’s d with a 95% confidence interval, the small-sample-corrected Hedges’ g, and the equivalent r.

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When to use this

Use this whenever you need a standardized mean difference: reporting your own two-group result (most journals and APA 7 require an effect size next to every t-test), extracting effect sizes from published papers for a meta-analysis (means, SDs and ns are usually all a paper gives you), or judging whether a statistically significant finding is practically meaningful. Because d is in standard deviation units it can be compared across studies that used different measurement scales.

Key assumptions

  • Two independent groups (for pre–post designs, d computed this way ignores the correlation between measures).
  • Pooled SD assumes roughly similar variances in the two groups.
  • Cohen's benchmarks (0.2 / 0.5 / 0.8) are conventions, not laws — field-specific norms matter more.

Common mistakes

  • Reporting d from tiny samples without the Hedges' correction — d is biased upward when n < 20 per group.
  • Treating a significant p-value as evidence of a large effect — significance reflects n as much as magnitude.
  • Comparing d values across studies whose control groups differ wildly in variability.

Frequently asked questions

What is the difference between Cohen's d and Hedges' g?
They estimate the same quantity. d divides by the pooled SD directly; g multiplies d by a correction factor J = 1 − 3/(4·df − 1) that removes the small-sample upward bias. With more than ~50 participants per group they are practically identical; with small samples report g.
How do I convert d to r or to an odds ratio?
This calculator reports the exact r for your group sizes (r = d/√(d² + a), a = (n1+n2)²/(n1·n2); a = 4 for equal groups). For a rough odds ratio, OR ≈ exp(1.81 × d). These conversions are standard in meta-analysis when studies report on different metrics.
Is a negative d a problem?
No — the sign only encodes which group you entered first. |d| carries the magnitude. Just make sure the sign convention is consistent (and stated) if you are extracting several effects for a synthesis.

Related free tools

Sample size calculatorSample size for two groupsConfidence intervalDescriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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