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Effect Size Converter

Convert between effect sizes — Cohen’s d, correlation r, odds ratio, log odds ratio, η² and Cohen’s f — plus the common-language effect size, U3, overlap and NNT.

Convert from

Effect size value

Group 1 size (for d ↔ r)

Group 2 size (for d ↔ r)

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How it works

r = d ÷ √(d² + a), a = (n₁ + n₂)² ÷ (n₁n₂) (= 4 for equal groups); d = r√a ÷ √(1 − r²); ln OR = d·π/√3; η² = r²; f = √[η² ÷ (1 − η²)]; CLES = Φ(d/√2); U3 = Φ(d); overlap = 2Φ(−|d|/2); NNT = 1 ÷ (2·CLES − 1)

Meta-analyses and power calculations often need an effect reported in one metric expressed in another. These are the standard conversions from Borenstein et al., Introduction to Meta-Analysis (2009, ch. 7): d ↔ r through the group-size factor a, and d ↔ odds ratio through the logistic distribution (Hasselblad & Hedges; Chinn, 2000). The common-language effect size is the chance that a random person from group 1 scores higher than one from group 2; the NNT follows Kraemer & Kupfer (2006).

Worked example

A Cohen’s d of 0.5 with two groups of 50 converts to r = 0.2425, an odds ratio of 2.4766 (ln OR 0.9069), η² = 0.0588 and a common-language effect size of 63.8% — a medium effect.

Sources: Borenstein et al. (2009), Introduction to Meta-Analysis — Converting among effect sizes · Chinn (2000), A simple method for converting an odds ratio to effect size, Statistics in Medicine

Frequently asked questions

Why do I need the group sizes?

The d-to-r conversion depends on how the sample is split. With equal groups a = 4 and r = d/√(d² + 4); unequal groups give a slightly smaller r for the same d.

How accurate is the odds ratio conversion?

It assumes the underlying continuous variable follows a logistic distribution, which is close to normal. It is the standard approximation in meta-analysis and is usually within a few percent.