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Cohen's d Effect Size Calculator

Compute Cohen's d, Hedges' g, Glass's delta, eta squared, and the 95% CI for the standardized mean difference between two groups in your browser.

Cohen's d effect size calculator

Compare two groups on a continuous outcome. Summary statistics mode accepts means, standard deviations, and sample sizes. Raw data mode accepts the actual numbers, one group per textarea.

Cohen's d is computed as (Group 1 mean - Group 2 mean) divided by the pooled SD. Positive means Group 1 is higher; negative means Group 2 is higher.

Summary statistics

Group 1

Group 2

The tool stores the SD in its sample (n - 1) form internally. When you switch the SD type selector, your typed value is interpreted in whichever convention you pick, and the converted sample SD is fed into the pooled-variance formula.

Effect size

Cohen's d (pooled SD)

0.6119

95% CI: [0.163, 1.06]

Medium (around 0.5). Sawilowsky: Medium (around 0.5).

Mean difference
+5.3

Group 1 mean minus Group 2 mean.

Pooled SD
8.6617

Square root of the (n - 1) weighted average of both sample variances.

Cohen's d
0.6119

Mean difference divided by pooled SD.

Hedges' g
0.606

d times the J(df) small-sample correction. J = 0.9904.

Glass's delta
0.5824

Mean difference divided by Group 2 SD only.

Cohen's d (population)
0.6119

Mean difference divided by the n-weighted (population) SD.

Eta squared (eta^2)
0.0876

Proportion of total variance explained by group membership.

Omega squared
0.0759

Less-biased relative of eta squared; zero when d is below the noise floor.

r (point-biserial)
0.2926

Correlation between group membership and outcome.

Degrees of freedom
78

n1 + n2 - 2.

Practical meaning

Common language ES
66.74%

Probability that a randomly chosen Group 1 value exceeds a randomly chosen Group 2 value.

Cohen's U3
72.97%

Percent of Group 1 that scores at or above the Group 2 mean.

Distribution overlap
75.96%

Area shared by two equal-variance normal curves with this d.

Group statistics in use

GroupnMeanSample SDPop. SD
Group 14075.48.28.0969
Group 24070.19.18.9855

Magnitude scales

Effect size thresholds are conventions, not laws. Both scales below are widely reported; pick the one that matches your field.

|d|Cohen (1988)Sawilowsky (2009)
0.01below smallvery small
0.20smallsmall
0.50mediummedium
0.80largelarge
1.20large (extended)very large
2.00large (extended)huge

Cohen's d vs Hedges' g

Cohen's d uses the pooled sample standard deviation. With small samples the estimate has a slight positive bias because the pooled SD itself is biased downward; the bias is roughly 3 / (4 * df - 1). Hedges' g multiplies d by the J correction to remove it. For df above about 50, g and d differ by less than one percent.

When to prefer Glass's delta

Glass's delta divides the mean difference by the control group's SD alone, not a pooled value. Use it when an intervention is expected to change variability as well as the mean (for example a tutoring program that lifts the bottom of a class), since pooling would mask the difference. Group 2 in this tool is treated as the control by convention.

What CLES and U3 mean

The Common Language Effect Size is the probability that a randomly picked person from Group 1 scores higher than a randomly picked person from Group 2. Cohen's U3 is the percentile of Group 2's mean within Group 1. Both translate d into a sentence anyone can read, which is why journals increasingly ask for them alongside the raw d.

Confidence interval caveats

The 95% CI shown here uses the standard normal approximation from Hedges and Olkin (1985). It is fine for moderate to large samples and matches the value reported by most stats packages. For very small samples (say under 20 per group) the exact noncentral t interval is wider, and a dedicated package such as R's effectsize or Python's pingouin should be preferred.

Worked example walkthrough

With the default summary statistics above (Group 1 mean 75.4, SD 8.2, n 40 versus Group 2 mean 70.1, SD 9.1, n 40), the pooled SD is sqrt(((40 - 1) * 8.2^2 + (40 - 1) * 9.1^2) / 78), which works out to roughly 8.66. The mean difference is 5.3, so Cohen's d is 5.3 / 8.66, about 0.612. The Hedges J(78) factor is roughly 0.990, so Hedges' g is about 0.606. Cohen would call that a medium-to-large effect; Sawilowsky would call it medium. The common language effect size is Phi(0.612 / sqrt(2)), about 66.6%: a randomly chosen Group 1 person beats a randomly chosen Group 2 person about two times out of three. Switching to raw data mode reproduces the same number from the underlying samples and is a useful sanity check when you have the original observations.

How to use

  1. Pick an input mode at the top. Summary statistics is the fastest if you already have the mean, SD, and n for each group. Raw data is useful when you have the underlying observations and want the means and SDs computed for you.
  2. Label your groups. Group 1 is the numerator of Cohen's d, so its mean is what gets compared against the Group 2 mean. Group 2 doubles as the control for Glass's delta.
  3. Enter the data. In summary mode, type each group's mean, standard deviation, and sample size. Set the SD type selector to match how your SD was computed (Excel STDEV.S or STDEV.P) so the pooled formula uses the right convention. In raw mode, paste the values for each group separated by commas, semicolons, line breaks, or whitespace.
  4. Read the effect size card. Cohen's d, Hedges' g, Glass's delta, eta squared, omega squared, and the point-biserial correlation are all shown with the 95% CI for d. The colored badge translates the magnitude into the Cohen (1988) and Sawilowsky (2009) scales.
  5. Check the Practical meaning panel for CLES, U3, and overlap. These convert d into the kind of sentence anyone can understand without statistical training.
  6. Click Copy summary to paste a clean multi-line report of the means, SDs, every effect size, the CI, and the interpretation into a paper, a Slack thread, or a lab notebook.

About this tool

Cohen's d Effect Size Calculator computes the standardized mean difference between two independent groups and reports every related effect size measure in a single readout, entirely in your browser. Two input modes are supported: a summary-statistics mode that accepts the mean, standard deviation, and sample size of each group, and a raw-data mode that accepts the underlying observations one group per textarea and computes the descriptive statistics for you. The result panel shows Cohen's d using the pooled sample standard deviation, Hedges' g with the J(df) small-sample correction (J = 1 - 3 / (4 df - 1)), Glass's delta which divides by the control-group SD alone for situations where the intervention is expected to change variability as well as the mean, the population variant of d that uses the n-weighted SD, eta squared and a less-biased omega squared, the point-biserial correlation between group membership and outcome, the mean difference and pooled standard deviation that feed into d, and the 95% confidence interval for d using the Hedges and Olkin (1985) approximate variance. Practical-meaning summaries are reported alongside the raw numbers: the Common Language Effect Size (probability that a randomly chosen Group 1 observation exceeds a randomly chosen Group 2 observation), Cohen's U3 (the percentile of Group 2's mean within Group 1's distribution), and the overlap area of two equal-variance normal curves with the calculated d. Both the original Cohen (1988) small / medium / large thresholds and the extended Sawilowsky (2009) scale (very small / small / medium / large / very large / huge) are shown so the reader can match the convention used in their field. The SD type selector handles the common mismatch between sample SD (n - 1, the default in R, SPSS, JASP, and Excel STDEV.S) and population SD (n, Excel STDEV.P) without the user having to convert by hand. A swap-groups control flips Group 1 and Group 2 in one click, which is useful when the sign of d came out the wrong way for the write-up. Useful for psychology, education, medical, and social-science researchers reporting effect sizes alongside p-values, growth and product teams interpreting A/B test results in standardized units, graduate students checking textbook problems, meta-analysts converting between effect size measures, and anyone who needs more than a t-test to describe how separated two groups really are. The visitor and group data you enter never leaves your browser.

Free to use. Works in your browser. No signup, no login.

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