Cohen’s d is a standardized measure of effect size for the difference between two means. It expresses the mean difference in units of standard deviation so the effect can be compared across outcomes.

How do you calculate Cohen’s d for two independent groups?

For two independent groups, d = (M₁ − M₂) / s_pooled where s_pooled assumes equal variances. The pooled SD is computed from both sample variances and shared degrees of freedom.

How do you interpret the magnitude of Cohen’s d?

Cohen’s benchmarks are d ≈ 0.2 (small), 0.5 (medium), and 0.8 (large). Use them as a general guide while considering practical significance.

What is the difference between Cohen’s d and Hedges’ g?

Hedges’ g applies a small-sample correction factor J to Cohen’s d, which makes g slightly smaller than d when sample sizes are low.

Can Cohen’s d be used for paired designs?

Yes. For paired or repeated measures you use the mean and SD of the difference scores, which reflects within-subject variability.

Cohen’s d Calculator (Effect Size)

Cohen’s d calculator for effect size between two means. Supports independent samples, one-sample and paired designs, with pooled SD, Hedges’ g, interpretation, and step-by-step working.

Design & inputs

Choose the study design and enter summary statistics. Fields accept dot or comma as decimal separators.

Group 1

Mean (M₁) Standard deviation (s₁) Sample size (n₁)

Group 2

Mean (M₂) Standard deviation (s₂) Sample size (n₂)

Direction of effect

Standardizer

Outcome / context (optional)

You can use dot or comma as decimal separators. All values must be positive where required.

Cohen’s d (effect size)

—

Hedges’ g = —

Interpretation: —

How to use this calculator

This calculator quantifies the magnitude of a difference between means. Choose the study design (two independent groups, one-sample comparison, or paired/repeated measures), input the summary statistics, and tap Calculate. The result displays Cohen’s d, the bias-corrected Hedges’ g, and a textual interpretation.

Methodology

The calculator mirrors the classical formulas used in statistics texts. For independent groups, it computes the pooled standard deviation unless you select one of the Glass alternatives, divides the mean difference by that SD, and then applies Hedges’ correction factor J = 1 − 3 / (4·df − 1). For one-sample and paired designs, it uses the sample SD or the SD of differences and the appropriate degrees of freedom. Refer to the formulas below for the exact equations.

Improve focus by keeping the direction and standardizer consistent with your research question.
Interpretation labels (≈0.2 small, 0.5 medium, 0.8 large) are conventions; consider practical significance.
If the denominator becomes very small, the effect size may be unstable—double-check your SD values.

Results are estimates. Always cross-check with original data, especially when sample sizes or variability are limited.

Should I use the pooled SD or one group’s SD? +

The classical Cohen’s d assumes equal variances and uses the pooled SD. Glass’s Δ variants use a single group’s SD when one group represents a stable reference.

Can I compute Cohen’s d from a t statistic? +

Yes. When only t and n are published, you can transform t into d, but this calculator focuses on means, SDs, and sample sizes for clarity.

What if the SD is zero or tiny? +

If the denominator is near zero, d becomes unstable. A zero SD means no variability, so the effect size is undefined and likely reflects data issues.

Is a statistically significant difference always large? +

No. Significance depends on sample size as well as effect size. Especially with large samples, even small d values can be significant, so report d alongside p-values.

Full original guide (expanded)

This section preserves the related resources and contextual guidance originally published with the calculator.

Core Math & Algebra tools

More statistics calculators

Formulas

Two independent groups:

d = (M₁ − M₂) / s_pooled

s_pooled = sqrt(((n₁ − 1)s₁² + (n₂ − 1)s₂²) / (n₁ + n₂ − 2))

One-sample comparison:

d = (M − μ₀) / s

Paired / repeated measures:

d = M_diff / s_diff

Hedges’ g:

g = J · d, where J = 1 − 3 / (4·df − 1)

Citations

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures

FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

0.1.0-draft — 2026-01-19: Initial audit spec draft and formula extraction (review required).
0.1.0-draft — Added references to NIST and FTC sources and preserved calculator explanations.

✓ Verified by Ugo Candido Last Updated: 2026-01-19 Version 0.1.0-draft

Version 1.5.0