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Cramér's V Calculator

Effect size for a contingency table — chi-square, degrees of freedom, p-value and Cramér's V (with the phi coefficient for 2×2).

Contingency table
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How it works

V = √[ χ² ÷ (n · (min(rows, columns) − 1)) ]; χ² = Σ (O − E)² ÷ E, E = row total × column total ÷ n

A chi-square test says whether two categorical variables are associated, but its size grows with the sample. Cramér's V rescales chi-square to a 0–1 effect size that is comparable across tables and sample sizes. For a 2×2 table it equals the phi coefficient. Thresholds shift with the smaller dimension — for df* = 1, 0.1/0.3/0.5 are small/medium/large; for larger tables the same V means a stronger association.

Worked example

A 3×3 table with n = 125: χ² = 47.6, df = 4, p < 0.0001, V = 0.44 — a medium-to-large association.

Frequently asked questions

V or the contingency coefficient?

Cramér's V reaches 1 for a perfect association in any table shape; Pearson's contingency coefficient cannot, so V is the better-behaved measure.

Does V have a direction?

No — it is always positive. Use the table itself (or odds ratios) to see which categories go together.

Related calculators

Chi-Square Calculator
Run a chi-square goodness-of-fit or test of independence — get the χ² statistic, degrees of freedom, p-value and a plain-language verdict at α = 0.05.
Fisher's Exact Test Calculator (2×2)
Exact p-value for a 2×2 table — one- and two-sided Fisher's exact test with the odds ratio, for small samples where chi-square is unreliable.
Cohen’s Kappa Calculator
Inter-rater agreement for two raters and two categories from a 2×2 table — observed agreement, expected agreement, κ and its interpretation.

For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.