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Degrees of Freedom Calculator

Calculate degrees of freedom for common statistical tests.

About Degrees of Freedom Calculator

Each parameter estimated from the data consumes one degree of freedom. That is why a sample variance divides by n − 1 rather than n: the mean has already been estimated from the same data. Using the wrong degrees of freedom shifts every critical value and p-value, and the error is largest in small samples where it matters most.

Formula

Degrees of Freedom

One sample: n − 1; two sample: n₁ + n₂ − 2; contingency: (r − 1)(c − 1)

degrees of freedom
Independent pieces of information available after estimating parameters

Worked example

With the default values below, Degrees of Freedom Calculator returns One-Sample Degrees of Freedom of 29. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample size 1minimum 1
30
Sample size 2minimum 0
25
Parameters estimatedaccepts 0–20
1
Rows in a contingency tableaccepts 1–30
3
Columns in a contingency tableaccepts 1–30
4

Results

One-Sample Degrees of Freedom
29
Two-Sample Pooled Degrees of Freedom
53
Regression Residual Degrees of Freedom
28
Contingency Table Degrees of Freedom
6
Paired-Sample Degrees of Freedom
24

Step by step

  1. 1Values used
  2. 2Degrees of Freedom
  3. 3One-Sample Degrees of Freedom= 29
  4. 4Two-Sample Pooled Degrees of Freedom= 53
  5. 5Regression Residual Degrees of Freedom= 28
  6. 6Contingency Table Degrees of Freedom= 6
  7. 7Paired-Sample Degrees of Freedom= 24

Assumptions and limits

  • The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Degrees of Freedom calculated?

One sample: n − 1; two sample: n₁ + n₂ − 2; contingency: (r − 1)(c − 1) Each parameter estimated from the data consumes one degree of freedom. That is why a sample variance divides by n − 1 rather than n: the mean has already been estimated from the same data.

Why does Degrees of Freedom matter?

Using the wrong degrees of freedom shifts every critical value and p-value, and the error is largest in small samples where it matters most.

What values do I need to enter?

This calculator takes 5 inputs: Sample size 1, Sample size 2, Parameters estimated, Rows in a contingency table, Columns in a contingency table. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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