Degrees of Freedom Calculator

Pick your statistical test and enter your sample sizes to get the correct degrees of freedom for looking up critical values or p-values.

Test type

Sample size 1 (or total N for ANOVA, or pairs)

Sample size 2 (two-sample t-test only)

Table rows (chi-square only)

rows

Table columns (chi-square only)

cols

Number of groups (ANOVA only)

groups

What degrees of freedom means

Degrees of freedom (df) is the number of independent values that are free to vary when estimating a statistic. It’s a required input for looking up critical values in t-distribution, chi-square, and F-distribution tables, and it directly affects how a p-value is calculated for a given test.

The formulas used

This calculator applies the standard formula for each common test: a one-sample or paired t-test uses df = n – 1; an independent two-sample t-test (equal-variance/pooled) uses df = n1 + n2 – 2; a chi-square test of independence uses df = (rows – 1) × (columns – 1); and a one-way ANOVA uses df-between = k – 1 and df-within = N – k, where k is the number of groups and N is the total sample size.

Choosing the wrong test type will give you the wrong degrees of freedom, so confirm your test design before reading a result off a statistical table.
This tool assumes standard, equal-variance assumptions; some variants (like Welch’s t-test) use a different, non-integer df formula.

For general educational and statistical-planning purposes only.

Last reviewed August 2026