Calculate Cramer’s V from contingency counts or chi-square results, with p-value, expected-count diagnostics, effect-size interpretation, and bias correction.

Enter 2–6 rows of counts, one row per line. Separate columns with spaces, commas or tabs.

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Cramer’s V Formula

Cramer’s V measures the strength of association between two categorical variables in a contingency table. Use observed counts or a Pearson chi-square statistic, sample size and both table dimensions to calculate V.

V = √((X²) / (n(k - 1)))
X² = V² × n × (k - 1)
n = (X²) / (V²(k - 1))
k = (X²) / (V²n) + 1
  • V = Cramer’s V
  • X² = chi-square value
  • n = total sample size
  • k = the smaller of the number of rows or columns in the contingency table

Choose Observed counts and paste equal-length rows, or choose Pearson chi-square results and enter the statistic, N, rows and columns. Select Calculate. Algebraic rearrangements below are reference identities, not additional calculator modes.

Cramer’s V Result Interpretation

Cramer’s V ranges from 0 to 1. A value near 0 means little or no association between the categorical variables. A value near 1 means a stronger association.

Cramer’s V General interpretation
0.00 No association
0.01 to 0.10 Very weak association
0.10 to 0.30 Weak association
0.30 to 0.50 Moderate association
0.50 to 1.00 Strong association

These historical cutoffs are rough descriptions, not universal thresholds. The calculator omits categorical effect-size labels; interpretation depends on the topic, sample size and table shape.

Contingency table size Rows Columns k = min(rows, columns)
2 by 2 2 2 2
3 by 2 3 2 2
4 by 3 4 3 3
5 by 5 5 5 5

Example Problems

Example 1: Calculate Cramer’s V

You have a chi-square value of 18.4, a total sample size of 200, and a 3 by 2 table. Enter rows = 3 and columns = 2; the smaller dimension is k = 2.

V = √((18.4) / (200(2 - 1)))
V = √(0.092) = 0.3033

Cramer’s V is approximately 0.3033.

Example 2: Calculate the Chi-Square Value

You have Cramer’s V = 0.25, sample size n = 320, and k = 4.

X² = 0.25² × 320 × (4 - 1)
X² = 0.0625 × 320 × 3 = 60

The chi-square value is 60.

FAQ

What does Cramer’s V tell you?

Cramer’s V tells you how strongly two categorical variables are associated. For example, it can measure the association between gender and survey preference, education level and voting category, or product type and customer response. It does not tell you that one variable causes the other.

What value should I use for k?

Use the smaller number of rows or columns in the contingency table. For a 4 by 3 table, k = 3. For a 2 by 5 table, k = 2. The formula uses k – 1, so k must be greater than 1.

Can Cramer’s V be greater than 1?

No. Cramer’s V should range from 0 to 1. If your result is greater than 1, check that the chi-square value, sample size, and k value were entered correctly. Also make sure k is the smaller table dimension, not the total number of cells.