What it does
Papers report effects in many ways: a t or F statistic, Cohen’s d, a correlation, an odds ratio or eta squared. To compare studies, pool them in a meta-analysis or plan a sample size, you need them on one scale. Type what you have and this tool shows every effect size it can be converted to, with confidence intervals where a standard one exists and a rough size label for each.
How to use it
- Pick what you are starting from in Start from.
- Type its value and the boxes that appear. Group sizes give intervals and make the conversions exact; a paired t test needs the number of pairs; an F test needs both degrees of freedom; a chi-square needs the total N.
- Read the table. Each row shows the value, its interval, a size label and how it was worked out. Download the table as a CSV, or the report as an image, PDF or Word file.
The conversions
- From t: d = t √(1/n1 + 1/n2) for two separate groups; dz = t / √n for paired data (the change measured against the spread of the changes, which is not the same scale as d).
- d and r: r = d / √(d² + a). With group sizes, a = N(N − 2)/(n1 n2), so r is exactly the point-biserial correlation t / √(t² + df); without them a = 4, the value for equal groups.
- d and odds ratios: ln OR = d π / √3, the logistic approximation (Hasselblad and Hedges). It assumes the yes/no outcome comes from cutting a continuous, roughly logistic scale.
- Hedges’ g = d × J, where J is the exact small-sample correction Γ(df/2) / (√(df/2) Γ((df − 1)/2)).
- From F: partial η² = F df1 / (F df1 + df2), partial ω² = df1 (F − 1) / (df1 (F − 1) + N) and Cohen’s f = √(η² / (1 − η²)). With df1 = 1 (two groups) d follows too.
- From chi-square: Cohen’s w = √(χ²/N) and Cramér’s V = w / √(m − 1), where m is the smaller side of the table. For a 2 × 2 table w is phi, used as r.
- Cliff’s delta, probability of superiority, U3, overlap and NNT come from d assuming two normal groups with the same spread: δ = 2Φ(d/√2) − 1.
The interval for d uses the usual standard error √((n1 + n2)/(n1 n2) + d²/(2(n1 + n2))); r uses Fisher’s z when you start from r. Intervals are carried through each conversion.
Worked example
A study reports t(43) = 2.5 with groups of 20 and 25. The tool gives d = 0.75 (95 % CI 0.1419 to 1.358), Hedges’ g = 0.7368, r = 0.3562, an odds ratio of 3.898 and η² = 0.1269: a medium-to-large effect by Cohen’s guide. Starting instead from F(2, 27) = 5.2 gives partial η² = 0.2781, partial ω² = 0.2188 and Cohen’s f = 0.6206.
Limits
Conversions between families (for example d to an odds ratio) rest on the assumptions above and are approximations. A chi-square with more than 1 degree of freedom, or an F with df1 above 1, cannot be turned into a single d. Intervals for eta squared from F need the noncentral F distribution and are not given. Signs cannot be recovered from F or chi-square: set them from the direction of the effect.
Frequently asked questions
Which should I report? The one that fits your analysis (d or g for two means, r for correlations, odds ratios for yes/no outcomes, η² or ω² for ANOVA), with its confidence interval.
Are Cohen’s labels reliable? They are rough. A “small” effect can matter a lot in medicine or education; compare with typical effects in your own field.
Is anything sent anywhere? No. Everything is worked out in your browser.
Run the test itself with the hypothesis test chooser and runner.
Where the numbers come from
- Formulas: Borenstein, Hedges, Higgins and Rothstein (2009), Introduction to Meta-Analysis; Lakens (2013), Frontiers in Psychology 4:863; McGraw and Wong (1992) for the common-language effect size.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.