About the Effect Size Calculator
This effect size calculator tells you how big a difference is, not just whether it is statistically significant. In two-group mode, enter each group’s mean, standard deviation and sample size to get Cohen’s d, the small-sample-corrected Hedges’ g, Glass’s Δ (using the control group’s SD), an approximate 95% confidence interval for d, the equivalent correlation r and eta squared. In ANOVA mode, enter the effect and error sums of squares with their degrees of freedom to get η², the less biased ω², Cohen’s f and the F statistic.
It is aimed at psychology, education, medical and social-science students and researchers who need to report effect sizes alongside p-values (as APA style requires), plan power analyses or compare results across studies in a meta-analysis. Each result comes with Cohen’s conventional label — small, medium or large — so you can describe it in words.
Cohen’s benchmarks (d = 0.2, 0.5, 0.8; η² = 0.01, 0.06, 0.14) are rough rules of thumb from the behavioural sciences; what counts as meaningful depends on your field. The calculations assume independent groups and roughly normal data.
With the default inputs, the effect size is 0.7318. Change any value above to recalculate instantly.
How to use the effect size calculator
- 1Choose two-group mode if you have means and SDs, or ANOVA mode if you have sums of squares.
- 2Enter the mean, standard deviation and sample size for each group — or the SS and df values.
- 3Read Cohen’s d (or η²) and its small/medium/large label.
- 4Report Hedges’ g for small samples and ω² for small ANOVA studies.
- 5Use the confidence interval to judge how precisely the effect is estimated.
Formula and method
Cohen’s d expresses the difference between two means in units of the pooled standard deviation. Hedges’ g multiplies d by a small-sample correction factor (Hedges’ approximation to the exact gamma-function correction), and Glass’s Δ divides by the control group’s SD alone, which is useful when a treatment changes the spread. The 95% interval uses the large-sample standard error √[(n₁+n₂)/(n₁n₂) + d²/(2(n₁+n₂))]. For two groups, η² = t² ÷ (t² + df) with t = d√(n₁n₂/(n₁+n₂)), and r = √η².
In ANOVA mode, η² is the share of total variability explained by the effect. Because η² is biased upward in small samples, ω² subtracts the variability expected by chance. Cohen’s f = √(η² ÷ (1 − η²)) is the effect size used in ANOVA power analysis, and F = (SS_effect/df_effect) ÷ (SS_error/df_error).
- M₁, M₂
- Group means (treatment, control)
- s₁, s₂
- Group standard deviations
- n₁, n₂
- Group sample sizes
- s_p
- Pooled standard deviation
- SS
- Sum of squares (effect, error, total)
- MS_error
- Mean square error, SS_error ÷ df_error
Worked examples
Teaching method: 78.4 vs 72.1, SDs 8.2 and 9.0, 25 per group
The pooled SD is √[(24 × 8.2² + 24 × 9²) ÷ 48] ≈ 8.609, so d = 6.3 ÷ 8.609 ≈ 0.73, a medium effect. The correction factor 1 − 3/191 gives g ≈ 0.720, and Glass’s Δ = 6.3 ÷ 9 = 0.70.
Unequal groups: 24.5 (SD 4.0, n 40) vs 22.0 (SD 4.5, n 35)
The pooled SD is about 4.240, so d = 2.5 ÷ 4.240 ≈ 0.59 (medium). With 73 degrees of freedom the Hedges correction is tiny, giving g ≈ 0.584, and the equivalent correlation is r ≈ 0.286.
One-way ANOVA: SS effect 120, SS error 480, df 2 and 57
η² = 120 ÷ 600 = 0.20, a large effect. MS error = 480 ÷ 57 ≈ 8.42, so ω² = (120 − 2 × 8.42) ÷ (600 + 8.42) ≈ 0.170 and F = 60 ÷ 8.42 = 7.125. Cohen’s f = √(0.2/0.8) = 0.5.
Frequently asked questions
How do you calculate Cohen’s d?+
Subtract one group mean from the other and divide by the pooled standard deviation, √[((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2)]. For means of 78.4 and 72.1 with a pooled SD of 8.61, d = 6.3 ÷ 8.61 ≈ 0.73.
What is a small, medium and large effect size?+
Cohen suggested d = 0.2 (small), 0.5 (medium) and 0.8 (large), and η² = 0.01, 0.06 and 0.14 for the same labels. They are conventions for the behavioural sciences, not strict thresholds, so compare with typical effects in your field.
What is the difference between Cohen’s d and Hedges’ g?+
Hedges’ g applies a correction factor of about 1 − 3/(4(n₁+n₂) − 9) because d slightly overestimates the population effect in small samples. With 20 per group the correction is about 2%; above 50 per group the two are nearly identical.
When should I use Glass’s delta?+
Use Glass’s Δ when the treatment may change the variability of scores, so pooling the SDs would be misleading. It standardises the mean difference by the control group’s standard deviation only.
What is the difference between eta squared and omega squared?+
η² is the proportion of variance explained in your sample and tends to overestimate the population value. ω² adjusts for that bias using the error mean square and is preferred for small samples; it is always slightly smaller than η².
Why report an effect size if my result is significant?+
A p-value only says whether an effect is likely to be non-zero; with a large sample even trivial differences are significant. The effect size shows how big the difference is and lets readers compare studies, which is why APA style asks for both.