Effect Size Calculator
Calculate Cohen's d, eta-squared, Cramér's V, or correlation effect sizes in seconds — with interpretation, 95% confidence intervals, and a copy-ready APA sentence.
Calculate Cohen's d, eta-squared, Cramér's V, or correlation effect sizes in seconds — with interpretation, 95% confidence intervals, and a copy-ready APA sentence.
Group 1
Group 2
For an independent t-test: df = n₁ + n₂ − 2
Cohen's d
Benchmarks (Cohen, 1988): 0.20 small · 0.50 medium · 0.80 large
Number of groups − 1
N − number of groups
Eta-squared (η²)
Benchmarks (Cohen, 1988): .01 small · .06 medium · .14 large
Rows × columns of your contingency table
Cramér's V
For a correlation test: df = N − 2
Correlation (r)
Benchmarks (Cohen, 1988): .10 small · .30 medium · .50 large · CI via Fisher z transformation
An effect size is a standardized number that tells you how big a difference or relationship is — not just whether it exists. A p-value can reach significance with a trivially small effect when the sample is large, and it can miss a substantial effect when the sample is small. That is why APA 7th edition and most thesis committees now require an effect size to be reported alongside every test statistic. If you want the full story, read our complete guide to effect sizes and why they matter.
The right measure depends on the statistical test you ran. Use this quick reference:
| Statistical test | Effect size | Small | Medium | Large |
|---|---|---|---|---|
| Independent / paired t-test | Cohen's d | 0.20 | 0.50 | 0.80 |
| ANOVA | η² / partial η² | .01 | .06 | .14 |
| Chi-square test | Cramér's V (2×2 table) | .10 | .30 | .50 |
| Correlation | Pearson / Spearman r | .10 | .30 | .50 |
Cohen's d expresses the difference between two group means in standard deviation units: a d of 0.50 means the groups differ by half a standard deviation, regardless of the measurement scale. Eta-squared tells you the proportion of variance in the outcome explained by your grouping factor in an ANOVA. Cramér's V measures the strength of association between two categorical variables from a chi-square test — note that its benchmarks shrink as the table gets larger, which this calculator handles automatically. Finally, the correlation coefficient r is its own effect size; squaring it gives the proportion of shared variance.
APA style places the effect size directly after the test statistic and p-value, for example: t(58) = 2.87, p = .006, d = 0.74. Values that cannot exceed 1 (such as r, η², and V) are written without a leading zero. This calculator generates that sentence for you — enter your statistics, click Calculate, and copy the APA-formatted line straight into your results chapter. Where a confidence interval is standard practice (Cohen's d and r), the 95% CI is included as well.
Remember that Cohen's benchmarks are conventions, not laws. A "small" effect can be practically important in medicine, and a "large" one may be unremarkable in psychophysics. Always interpret the number in the context of your field and prior studies.
Calculate the exact sample size needed for your study design.
Answer a few questions to find the right test for your data.
Get a plain-English explanation of your p-value with APA formatting.
Generate perfectly formatted APA 7th edition results sentences.
Upload your data to Academic Stats Agent and get the correct test, effect sizes, and a publication-ready APA report — in minutes.
Try Academic Stats Agent — Free