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Effect Size Calculator (Cohen's d)

Measure how large the difference between two group means is in standard-deviation units. Enter the means, standard deviations and sample sizes, or paste the raw data, to get Cohen's d, the bias-corrected Hedges' g, Glass's Δ, a confidence interval and a plain-language interpretation.

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Input
Group 1 (treatment)
Group 2 (control)
Enter your values to see the result.
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How to use the Effect Size Calculator (Cohen's d)

  1. Choose the input: summary statistics or raw data for two groups.
  2. Enter mean, SD and n for group 1 (e.g. treatment) and group 2 (e.g. control), or paste each group's values.
  3. Pick the confidence level for the interval.
  4. Read Cohen's d and its interpretation; use Hedges' g for small samples.
  5. Copy the results for your report, e.g. “d = 0.54, 95% CI [0.03, 1.06]”.

Effect size formulas

MeasureFormulaWhen to use
Cohen's d(x̄₁ − x̄₂) ÷ s_p, s_p = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2))Default for two independent groups with similar SDs
Hedges' gd × J, J = Γ(df/2) ÷ (√(df/2) Γ((df−1)/2)) ≈ 1 − 3 ÷ (4df − 1)Small samples, meta-analysis
Glass's Δ(x̄₁ − x̄₂) ÷ s₂Treatment changes the spread; control SD as the yardstick
d_av(x̄₁ − x̄₂) ÷ √((s₁² + s₂²) ÷ 2)Unweighted average SD, e.g. unequal group sizes
r from dd ÷ √(d² + (n₁+n₂)² ÷ (n₁n₂))Reporting as a correlation

Example: means 78 and 72, SDs 10 and 12, 30 per group. s_p = √((29 × 100 + 29 × 144) ÷ 58) = 11.05, so d = 6 ÷ 11.05 = 0.54, a medium effect.

What an effect size means in practice

dLabelGroup 2 below the group 1 mean (U₃)Overlap of the two distributions
0.2Small57.9%92.0%
0.5Medium69.1%80.3%
0.8Large78.8%68.9%
1.2Very large88.5%54.9%
2.0Huge97.7%31.7%

A p-value tells you whether a difference is likely to be real; an effect size tells you how big it is. Large samples can make tiny effects “significant”, so report both.

Frequently asked questions

How is Cohen's d calculated?

d = (x̄₁ − x̄₂) ÷ s_p, where the pooled standard deviation s_p = √(((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2)). It expresses the difference between the means in standard-deviation units.

What counts as a small, medium or large effect?

Cohen's widely used rules of thumb are |d| ≈ 0.2 small, 0.5 medium and 0.8 large; Sawilowsky added 1.2 very large and 2.0 huge. These are rough guides only; what matters in practice depends on the field and the cost of the outcome.

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

Cohen's d slightly overestimates the population effect in small samples. Hedges' g multiplies d by a correction factor J ≈ 1 − 3 ÷ (4(n₁ + n₂) − 9), which is close to 1 for large samples. Use g when groups have fewer than about 20 people each or in meta-analyses.

When should I use Glass's delta?

Glass's Δ divides the mean difference by the control group's standard deviation only. It is useful when the treatment is expected to change the spread of scores, or when the group SDs are very different.

Can Cohen's d be negative?

Yes. The sign only shows direction: a negative d means group 2 has the higher mean. The size of the effect is judged by the absolute value |d|.

How do I convert Cohen's d to r?

r = d ÷ √(d² + (n₁ + n₂)² ÷ (n₁n₂)), which simplifies to d ÷ √(d² + 4) for equal group sizes. For example d = 0.5 corresponds to r ≈ 0.24.

How is the confidence interval for d computed?

The calculator uses the standard large-sample approximation SE(d) = √((n₁ + n₂) ÷ (n₁n₂) + d² ÷ (2(n₁ + n₂))) and d ± z × SE. If the interval excludes 0, the difference is significant at the matching level.

Are all the tools on FreeToolCabin tested for quality and accuracy?

Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.

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