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Cohen's d Effect Size Calculator
Computes the standardised difference between two group means with the pooled standard deviation (Cohen's d), the small-sample corrected Hedges' g, Glass's Δ and the common-language effect size, with Cohen's small/medium/large interpretation.
When to use
You want to express how large the difference between two groups is in standard-deviation units, e.g. for reporting alongside a t-test, power analysis or meta-analysis.
Do not use when: You need to know whether the difference is statistically significant (use t-test), the outcome is binary (use odds-ratio), or the groups are paired (d for paired designs uses the SD of the differences).
Formula
pooled_sd = √(((n_a − 1)·sd_a² + (n_b − 1)·sd_b²) / (n_a + n_b − 2)); d = (mean_a − mean_b) / pooled_sd; g = d × (1 − 3 / (4(n_a + n_b) − 9)); Δ = (mean_a − mean_b) / sd_b; CLES = Φ(d / √2)
Hedges' correction uses the Hedges (1981) approximation of the exact gamma-function factor (difference below 0.1 % for n_a + n_b ≥ 20). Cohen's benchmarks are conventions, not thresholds of practical importance.
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
mean_a | number | yes | Sample mean of the first (treatment) group. | |
sd_a | number | yes | Sample standard deviation (n − 1) of group A. Range: > 0 | |
n_a | integer | yes | Sample size of group A. Range: ≥ 2 | |
mean_b | number | yes | Sample mean of the second (control) group. | |
sd_b | number | yes | Sample standard deviation of group B (used alone for Glass's Δ). Range: > 0 | |
n_b | integer | yes | Sample size of group B. Range: ≥ 2 |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
cohens_d | number | (mean_a − mean_b) / pooled SD. Positive when A is higher. | |
hedges_g | number | d × (1 − 3 / (4(n_a + n_b) − 9)): bias-corrected d for small samples. | |
glass_delta | number | (mean_a − mean_b) / sd_b: uses only the control group's SD. | |
pooled_sd | number | √(((n_a − 1) sd_a² + (n_b − 1) sd_b²) / (n_a + n_b − 2)). | |
mean_difference | number | mean_a − mean_b in the original units. | |
common_language_effect_size | number | Φ(d / √2): probability that a random member of A scores higher than a random member of B (normal, equal variances). | |
interpretation | string | Cohen's benchmarks on |d|: < 0.2 negligible, 0.2 small, 0.5 medium, 0.8 large. |
Example
105 vs 100, SD 15, n = 30 each: {"mean_a":105,"sd_a":15,"n_a":30,"mean_b":100,"sd_b":15,"n_b":30} → {"cohens_d":0.3333,"hedges_g":0.329,"glass_delta":0.3333,"pooled_sd":15,"mean_difference":5,"common_language_effect_size":0.5932,"interpretation":"Small"}
12 (SD 2, n 20) vs 10 (SD 3, n 25): {"mean_a":12,"sd_a":2,"n_a":20,"mean_b":10,"sd_b":3,"n_b":25} → {"cohens_d":0.7675,"hedges_g":0.754,"glass_delta":0.6667,"pooled_sd":2.6059,"common_language_effect_size":0.7063,"interpretation":"Medium"}
GET https://tttkmbb.com/api/v1/calculate/cohens-d?mean_a=105&sd_a=15&n_a=30&mean_b=100&sd_b=15&n_b=30
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/cohens-d(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/cohens-d · Markdown: https://tttkmbb.com/statistics/cohens-d.md · JSON definition: https://tttkmbb.com/statistics/cohens-d.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="cohens-d" - OpenAPI operationId:
calculate_cohens_d - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
FAQ
d or g?
They differ only by the small-sample correction; report Hedges' g when either group has fewer than about 20 observations, otherwise the two are practically identical.
When is Glass's Δ preferred?
When the intervention changes the spread of the treated group, so the control group's SD is the better yardstick.
Can d be larger than 1?
Yes. d is a ratio of the mean difference to the SD and is unbounded; d = 1 means the means are one standard deviation apart.
Related calculators
- T-Test Calculator — Test whether the same difference is statistically significant.
- Descriptive Statistics Calculator — Get each group's mean and SD from raw data.