Calculator inputs
Choose a design, enter summary statistics, and compute standardized effect size instantly.
Example data table
Use these sample figures to test the page and compare how different designs change the standardized effect size.
| Scenario | Inputs | Approximate result | Meaning |
|---|---|---|---|
| Independent groups | Mean1 24.6, SD1 4.8, n1 42; Mean2 20.3, SD2 5.1, n2 38 | d ≈ 0.87 | Large difference favoring Group 1 |
| Paired scores | Mean A 61, SD A 8; Mean B 68, SD B 7.5; pairs 30; r 0.55 | dz ≈ 0.86 | Large improvement after the paired condition |
| One-sample benchmark | Sample mean 112, SD 15, n 50; benchmark 100 | d ≈ 0.80 | Large difference above the benchmark |
Formula used
Cohen's d standardizes the mean difference by a relevant standard deviation. This makes results easier to compare across scales.
Independent samples
Pooled SD = √[((n1−1)s1² + (n2−1)s2²) ÷ (n1+n2−2)]
Cohen's d = (M1 − M2) ÷ Pooled SD
Hedges' g = J × d, where J = 1 − 3 ÷ (4N − 9)
Paired samples
SD of differences = √[s1² + s2² − 2rs1s2]
Cohen's dz = (MB − MA) ÷ SD of differences
One-sample benchmark
Cohen's d = (Sample Mean − Benchmark Mean) ÷ Sample SD
Helpful interpretation aids
This page also reports Hedges' g, approximate confidence intervals, equivalent correlation, common language effect size, U3, overlap, and t-equivalent values.
How to use this calculator
- Select the study design that matches your data structure.
- Enter means, standard deviations, and sample sizes.
- For paired samples, add the within-pair correlation.
- For one-sample mode, enter the benchmark mean.
- Choose the number of decimals for reporting.
- Press the calculate button to display results above the form.
- Review the direction note, interpretation band, and full metric table.
- Download a CSV or PDF summary for reports or appendices.
FAQs
1) What does Cohen's d measure?
Cohen's d measures the standardized distance between two means, or between a sample mean and a benchmark. It expresses the difference in standard deviation units, making results easier to compare across studies and scales.
2) When should I use the independent mode?
Use independent mode when two unrelated groups are compared, such as treatment versus control or two different classes. The calculator pools both group variances to estimate a shared standard deviation before computing d.
3) When should I use the paired mode?
Use paired mode for repeated measures or matched pairs, such as before-and-after scores for the same participants. The correlation matters because it changes the standard deviation of the difference scores and therefore the effect size.
4) What is Hedges' g?
Hedges' g is a small-sample corrected version of Cohen's d. It slightly shrinks the estimate when sample sizes are limited, giving a less biased standardized effect size for reporting and meta-analytic work.
5) How do I interpret small, medium, and large values?
A common rule is 0.2 for small, 0.5 for medium, and 0.8 for large. These are general guides only. Field-specific conventions, study design, and practical importance should always shape interpretation.
6) Why can the sign be negative?
The sign depends on subtraction order. A negative effect simply means the second condition, comparison group, or benchmark is larger than the first one. Magnitude still reflects the size of the standardized difference.
7) What does common language effect size mean?
Common language effect size estimates the probability that a randomly chosen score from one distribution exceeds a randomly chosen score from the comparison distribution. It turns d into a more intuitive probability-style summary.
8) Can I report this calculator result directly in research writing?
Yes, but you should also report the study design, group statistics, confidence interval, correction choice, and interpretation context. For formal research, match the exact effect size convention required by your journal, discipline, or supervisor.