Cohen's d Calculator - Effect Size for Two Groups
Calculate Cohen's d to quantify the standardized difference between two group means — get pooled SD, effect size, and an interpretive label instantly.
Enter the mean, standard deviation, and sample size for each group, then click Calculate to see Cohen's d with an effect-size interpretation.
Cohen's d Calculator - Effect Size for Two Groups
Calculate Cohen's d to quantify the standardized difference between two group means — get pooled SD, effect size, and an interpretive label instantly.
Group 1 Data
Group 2 Data
About the Cohen's d Calculator
Cohen's d is the most widely used measure of effect size for comparing the means of two independent groups. Introduced by the statistician Jacob Cohen in his landmark 1969 book Statistical Power Analysis for the Behavioral Sciences, it expresses the difference between two means in terms of the pooled standard deviation. The result is a dimensionless number that sits on a common scale regardless of what was measured — test scores, reaction times, blood pressure readings, or revenue per user.
The formula is straightforward: d = (M₁ − M₂) / s_pooled, where s_pooled is the square root of the weighted average of the two sample variances. This pooled standard deviation accounts for the fact that the two groups may have different sample sizes. The sign of d conveys direction: a positive d means Group 1 has a higher mean, a negative d means Group 2 does.
Jacob Cohen proposed a conventional benchmark that has since become standard across the social and biomedical sciences. An absolute d below 0.2 is considered negligible — the groups are so similar that the difference is practically invisible in the data. A d between 0.2 and 0.5 is small but real; it corresponds roughly to the kind of overlap you see when comparing the heights of 15- and 16-year-old boys. A d between 0.5 and 0.8 is medium, comparable to the mean IQ difference between clerical and semi-skilled workers in Cohen's original analyses. A d above 0.8 is large and corresponds to easily observable differences, such as the gap in height between 13- and 18-year-old boys.
These benchmarks should be treated as heuristics rather than hard rules. In certain domains, a small effect size has enormous practical importance. A drug that reduces mortality by even a small absolute amount in a population of millions creates a very large public health benefit. Conversely, a large effect size on a poorly constructed questionnaire may not translate to meaningful real-world differences. Always interpret d alongside confidence intervals, sample size, and domain knowledge.
Cohen's d is closely related to other effect size measures. Hedges' g uses a bias-corrected version of the pooled standard deviation and is preferred for small samples (n < 20 per group). Glass's Δ divides by the standard deviation of the control group only, which is useful when the two groups are expected to have inherently different variances. For effect sizes in more complex designs — correlation, ANOVA, regression — the equivalent measures are Pearson's r, η² (eta-squared), and partial η², respectively.
Practically, Cohen's d is most commonly encountered in power analysis, meta-analysis, and research reporting. In power analysis, knowing an expected effect size lets you calculate the sample size needed to detect the effect with a specified probability (power). In meta-analysis, d values from multiple studies can be averaged and weighted to produce a pooled estimate of the true effect. In clinical research, reporting d alongside p-values has become a requirement in many journals because a result can be statistically significant (p < 0.05) yet trivially small in effect size when the sample is very large.
Cohen's d Examples
Four scenarios from education, medicine, psychology, and marketing illustrating how to interpret effect size.
| Groups (M, SD, n) | Cohen's d | Interpretation |
|---|---|---|
| G1: M=85, SD=10, n=30 vs G2: M=80, SD=9, n=30 | d ≈ 0.52 | Medium effect. The new teaching method produces a meaningfully higher test score than the control group. |
| G1: M=120, SD=15, n=50 vs G2: M=130, SD=16, n=50 | d ≈ −0.65 | Medium effect (negative). The drug group has lower blood pressure than the placebo group — a favourable clinical outcome. |
| G1: M=450, SD=50, n=25 vs G2: M=500, SD=55, n=25 | d ≈ −0.95 | Large effect. Caffeine produces a substantial reduction in reaction time compared to the no-caffeine group. |
| G1: M=75.50, SD=20, n=100 vs G2: M=70.25, SD=18, n=100 | d ≈ 0.28 | Small effect. Layout A lifts average purchase value slightly — statistically detectable but modest in practical terms. |
How to Use the Cohen's d Calculator
- Enter the mean (M), standard deviation (s), and sample size (n) for Group 1 in the left panel.
- Enter the same three values for Group 2 in the right panel. Sample sizes must be at least 2.
- Click Calculate. The calculator displays the pooled standard deviation, Cohen's d, and an interpretive label (negligible / small / medium / large).
- Use the example buttons to load pre-built scenarios from education, medical research, and psychology.
- Click Reset to clear all fields and start a new calculation.
Cohen's d FAQ
What is a good Cohen's d value?
Cohen's conventional benchmarks are d = 0.2 (small), 0.5 (medium), and 0.8 (large). However, 'good' depends on context. In cognitive psychology, effects of d = 0.3 are often considered meaningful. In medicine, a small d on a life-saving intervention may be highly important. Always interpret d in the context of your domain's typical effect sizes and the practical consequences of the finding.
What is the pooled standard deviation?
The pooled standard deviation combines the variance from both groups into a single estimate of within-group spread, weighted by each group's degrees of freedom (n − 1). It is the denominator in the Cohen's d formula. Using pooled SD rather than just one group's SD ensures the effect size is not distorted when the two groups have different sample sizes or moderately different variances.
When should I use Hedges' g instead of Cohen's d?
Hedges' g applies a small-sample bias correction to Cohen's d. The difference is negligible for n > 20 per group but can be meaningful for smaller samples. If either group has fewer than 20 observations, reporting Hedges' g is recommended. The correction factor is approximately (1 − 3 / (4(n₁+n₂) − 9)), which you can multiply by the Cohen's d value this calculator produces.
Does Cohen's d assume equal variances?
The standard pooled-SD formula implicitly assumes that the two population variances are roughly equal (homogeneity of variance). If the variances are very different, consider using Glass's Δ, which divides only by the control group's standard deviation, or report separate effect sizes for each comparison. A Levene's test or simple visual inspection of the two SDs can help you assess whether the assumption is reasonable.
Can Cohen's d be negative?
Yes. A negative d simply means Group 2 has a higher mean than Group 1. The sign reflects the direction of the difference, not the magnitude. In many research designs, the sign is arbitrary — it depends on which group you labeled Group 1. The absolute value of d is what matters for interpreting effect size, while the sign tells you which group scored higher.
How does effect size relate to statistical significance?
Statistical significance (p-value) tells you whether an effect is unlikely to have arisen by chance. Effect size (Cohen's d) tells you how large the effect is. A result can be highly significant (very small p) but trivially small in effect size when the sample is enormous. Conversely, a large effect size may fail to reach significance in a small sample. Reporting both the p-value and Cohen's d gives a complete picture of the strength and reliability of the finding.