Calculate Cramer’s V, chi-square, sample size, or rows or columns in a contingency table by entering any three values and solving for the missing one.

Cramer’s V Calculator

Enter any 3 values to calculate the missing variable

Related Calculators

Cramer’s V Formula

Cramer’s V measures the strength of association between two categorical variables in a contingency table. The calculator uses the chi-square statistic, total sample size, and the smaller table dimension to solve for the missing value.

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

To calculate Cramer’s V, enter the chi-square value, sample size, and k. To work backward, leave one field blank and enter the other three values. The calculator rearranges the same formula to solve for the missing chi-square value, sample size, table dimension, or Cramer’s V.

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 cutoffs are general guidelines. The practical meaning of the result depends on the topic, sample size, and table shape.

Contingency table size Rows Columns k value to enter
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. Since the smaller dimension is 2, use 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.