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.

Group 1

Group 2

For an independent t-test: df = n₁ + n₂ − 2

Cohen's d

APA-formatted result

Benchmarks (Cohen, 1988): 0.20 small · 0.50 medium · 0.80 large

Number of groups − 1

N − number of groups

Eta-squared (η²)

APA-formatted result

Benchmarks (Cohen, 1988): .01 small · .06 medium · .14 large

Rows × columns of your contingency table

Cramér's V

APA-formatted result

For a correlation test: df = N − 2

Correlation (r)

APA-formatted result

Benchmarks (Cohen, 1988): .10 small · .30 medium · .50 large · CI via Fisher z transformation

What Is an Effect Size?

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.

Which Effect Size Should You Report?

The right measure depends on the statistical test you ran. Use this quick reference:

Statistical testEffect sizeSmallMediumLarge
Independent / paired t-testCohen's d0.200.500.80
ANOVAη² / partial η².01.06.14
Chi-square testCramér's V (2×2 table).10.30.50
CorrelationPearson / 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.

How to Report Effect Sizes in APA Style

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.

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