Cohen's d Calculator

StatisticsLast updated: August 22, 2026

Cohen's d divides the difference between two group means by the pooled standard deviation, which frees the difference from its unit of measurement. "The treatment group scored 6.4 points higher" says nothing to a reader who does not know the scale; "d = 1.15" says the difference is larger than the within-group variability itself. That is why d is the common currency of meta-analysis and APA reporting.

This calculator compares two independent groups from raw data or from nothing more than the mean, standard deviation, and sample size of each group. It returns the pooled standard deviation, Cohen's d, the small-sample-corrected Hedges g, Glass delta (which uses the control group's standard deviation), and a confidence interval for d. It also reports intuitive equivalents such as distribution overlap, the superiority index (U₃), and the common language effect size (CLES).

If a paper gives you only means and standard deviations, choose the summary input.
Observations of the treatment or intervention group. Cohen's d is positive when it favors this group.
Observations of the comparison or control group. Glass delta uses this group's standard deviation.
The probability that the interval covers the true parameter.

Cohen's d and Its Variants

Pooled SD:       sₚ = √[ ((n₁−1)·s₁² + (n₂−1)·s₂²) / (n₁ + n₂ − 2) ]
Cohen's d:       d = (x̄₁ − x̄₂) / sₚ
Correction:      J = 1 − 3 / (4·df − 1),   df = n₁ + n₂ − 2
Hedges g:        g = J · d
Glass delta:     Δ = (x̄₁ − x̄₂) / s₂
Standard error:  SE(d) = √[ (n₁+n₂)/(n₁·n₂) + d² / (2(n₁+n₂)) ]
Confidence int.: d ± z₁₋α/₂ · SE(d)
Relation to t:   d = t · √(1/n₁ + 1/n₂)
Superiority:     U₃ = Φ(d),   CLES = Φ(d / √2),   OVL = 2·Φ(−|d|/2)

The pooled standard deviation is the square root of the degrees-of-freedom-weighted average of the two group variances, which assumes the variances are roughly equal. When they differ markedly, Glass delta is preferred.

How to Calculate

  1. If you have raw data, paste each group's observations into its own box; if you only have the summary from a paper, set the input format to "Summary statistics" and enter the mean, standard deviation, and n.
  2. Put the treatment or intervention group in group 1 and the control group in group 2: the sign of d follows that order.
  3. Choose the confidence level; 95% is the standard choice.
  4. Check the pooled standard deviation step — it is the denominator of d and the weighted average of the two group variances.
  5. Read Hedges g alongside Cohen's d; with a small sample, g is the value you should report.
  6. Judge the practical meaning of the effect from whether the confidence interval includes zero and from the overlap of the distributions.

Worked Examples

Comparing two groups from raw data

The treatment group averages 83.90 (s = 5.11) and the control group 73.90 (s = 3.90). With a pooled standard deviation of 4.54, Cohen's d = 10 / 4.54 = 2.200, a very large effect. Hedges g = 2.107, Glass delta = 2.564, and the 95% confidence interval is [1.090; 3.311]; the two distributions overlap by only 27.1%.

Cohen d: 2.200 · Effect size interpretation: Large · 95% confidence interval for Cohen d: [1.090; 3.311]

Effect size from a paper's summary statistics

Computing from the summary alone, with no raw data: the 5.70-point difference divided by a pooled standard deviation of 14.85 gives Cohen's d = 0.384, a small effect. The 95% confidence interval [0.020; 0.748] excludes zero, but its lower bound sits so close to zero that the effect could still be negligible. The corresponding test is t(116) = 2.085 with p = 0.039.

Cohen d: 0.384 · Effect size interpretation: Small · 95% confidence interval for Cohen d: [0.020; 0.748]

A small effect that is not significant

A 1.80-unit difference divided by a pooled standard deviation of 10.00 gives Cohen's d = 0.180, a negligible effect. The 95% confidence interval [-0.376; 0.735] includes zero and t(48) = 0.636 gives p = 0.528: there is neither statistical significance nor practical importance. The distributions overlap by 92.8%.

Cohen d: 0.180 · Effect size interpretation: Negligible · 95% confidence interval for Cohen d: [-0.376; 0.735]

Frequently Asked Questions

How large does Cohen's d have to be to count as large?
By Cohen's (1988) rule of thumb, 0.20 is small, 0.50 medium, and 0.80 large, while anything below 0.20 is usually treated as negligible. These thresholds are not universal: 0.40 can be noteworthy for an educational intervention, whereas in drug trials even an effect of 0.20 may be clinically important. Interpret them against the typical effect sizes in your own field.
What is the difference between Cohen's d and the p-value?
The p-value measures how likely the observed difference is under chance and shrinks as the sample grows; d measures the size of the difference and is unaffected by sample size. In a very large sample even a meaningless difference of d = 0.05 can come out at p < 0.001. That is why APA requires an effect size to be reported alongside p.
Should I report Hedges g or Cohen's d?
When the total sample is below 20, Cohen's d systematically overstates the true effect and Hedges g should be reported instead. As the sample grows the correction factor J approaches one and the two values become practically identical. Standard practice in meta-analysis is to convert every study to g before pooling.
When is Glass delta used?
When the intervention changes not only the mean but also the variability, the pooled standard deviation becomes misleading; Glass delta then uses only the control group's standard deviation as the denominator, expressing the effect on a scale untouched by the intervention. If Levene's test rejects equality of variances, Glass delta or a Welch-type version of Cohen's d is preferred.
Do SPSS and R give the same result?
Yes. SPSS 27 and later report Cohen's d, the Hedges correction, and Glass delta in the independent samples t-test output using the formulas applied here; in R, cohen.d() from the effsize package with hedges.correction = TRUE gives the same values. Small differences can arise only from the confidence interval method: this tool uses the Hedges-Olkin approximate standard error, while some software relies on the noncentral t distribution.
Does the same formula apply to paired (dependent) measurements?
No. For pre-post measurements there are two main options: d_z, which divides by the standard deviation of the differences, and d_av, which divides by the common standard deviation of the measurements. d_z inflates the effect when the measurements are highly correlated and cannot be compared directly with a d from independent groups. This tool is for two independent groups; in a paired design, always state which denominator you used.
What does a negative Cohen's d mean?
Only the direction of the difference: the mean of group 1 is lower than that of group 2. The magnitude of the effect is read from the absolute value, so d = −0.80 and d = 0.80 are equally large effects in opposite directions. Unless your report states the order in which the groups were entered, the sign is meaningless to the reader.