Effect Size Calculator — Cohen's d, r, η², Odds Ratio
Enter a Cohen's d, Pearson r, or an independent-samples t-statistic to instantly convert between all common effect size metrics — d, r, η², Cohen's f, the odds ratio, and probability of superiority.
Input type
Standardised mean difference — sign indicates direction
- 1
Absolute effect |d|
|0.5| = 0.5 - 2
Cohen's d
0.5000Sign indicates which group scored higher.
How does this calculator work?
Enter a Cohen's d, Pearson r, or t-statistic to convert between effect size metrics. d = 2r/√(1−r²); η² = r²; f = d/2; OR ≈ exp(π|d|/√3); probability of superiority = Φ(|d|/√2). Benchmarks: d < 0.2 negligible, 0.2–0.5 small, 0.5–0.8 medium, ≥ 0.8 large.
Formula
How this is calculated
Effect size metrics all measure the magnitude of a difference or relationship on a standardised scale, so results from studies using different raw units can be compared. Cohen's d (standardised mean difference) is the most common — dividing the group mean difference by the pooled standard deviation — and is the central value here. All other metrics convert from d using established algebraic identities.
Pearson r converts via r = d / √(d² + 4) (assuming equal group sizes). Eta-squared (η²) equals r², representing the proportion of variance explained. Cohen's f = |d|/2, used mainly in power analysis for ANOVA. The odds ratio approximation OR ≈ exp(π·|d|/√3) assumes the outcome follows a logistic distribution; it is a convenient approximation widely used in meta-analysis. Probability of superiority P = Φ(|d|/√2) is the probability that a randomly chosen person from group 1 scores higher than a randomly chosen person from group 2.
When you enter a t-statistic, d is derived from d = t × √(1/n₁ + 1/n₂). The Pearson r path uses the exact inverse relationship. Conventions from Cohen (1988): |d| < 0.2 = negligible, 0.2–0.5 = small, 0.5–0.8 = medium, ≥ 0.8 = large — but these are rough benchmarks and differ by discipline.
Frequently asked questions
Cohen's d expresses the mean difference in standard-deviation units and can exceed 1. Eta-squared (η²) is the proportion of total variance explained by the group factor — it ranges from 0 to 1 and equals r² for a two-group comparison. Small: η² ≈ 0.01; medium: 0.06; large: 0.14 (Cohen's benchmarks).
The logistic distribution has variance π²/3. The approximation maps a standardised normal effect (Cohen's d) onto a log-odds scale using the relationship OR = exp(d × π/√3). It is an approximation — the exact OR depends on the shape of the outcome distribution — but it performs well for typical social-science and medical studies.
Use 'Cohen's d (direct)' if you already have d from a paper or previous calculation. Use 'Pearson r' if you ran a correlation analysis. Use 't-statistic' if you have the raw t value and sample sizes from an independent-samples t-test — this path derives d as t × √(1/n₁ + 1/n₂) and also gives the exact r = t / √(t² + df).
Also known as
TG we-Calculate Editorial Team. (2026). Effect Size Calculator — Cohen's d, r, η², Odds Ratio [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/effect-size-calculator
TG we-Calculate Editorial Team. "Effect Size Calculator — Cohen's d, r, η², Odds Ratio." TG we-Calculate. 2026. https://we-calculate.com/calculator/effect-size-calculator.
TG we-Calculate Editorial Team, "Effect Size Calculator — Cohen's d, r, η², Odds Ratio," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/effect-size-calculator
@misc{wecalculate_effect_size_calculator, title = {Effect Size Calculator — Cohen's d, r, η², Odds Ratio}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/effect-size-calculator}}, year = {2026}, note = {TG we-Calculate} }
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