Chi Square Distribution Calculator

Work out chi square distribution instantly with clear inputs, formula shown and shareable results.

About Chi Square Distribution Calculator

The chi-square distribution is the sum of squares of independent standard normals, with mean equal to its degrees of freedom and variance twice that. It underpins goodness-of-fit and variance tests.

Formula

Chi-square CDF

P(X ≤ x) = P(df/2, x/2), the regularised lower incomplete gamma

Worked example

With the default values below, Chi Square Distribution Calculator returns P(X > x) — the p value of 0.0500096186. Change any input above and every figure here is recalculated in your browser.

Inputs used

Chi-square valueminimum 0: 11.07
Degrees of freedomaccepts 1–1,000: 5

Results

P(X > x) — the p value: 0.0500096186
P(X ≤ x): 0.9499903814
Critical value at 5%: 11.070498
Mean (equals the degrees of freedom): 5

Step by step

1Values used
2Chi-square CDF
3P(X > x) — the p value= 0.0500096186
4P(X ≤ x)= 0.9499903814
5Critical value at 5%= 11.070498
6Mean (equals the degrees of freedom)= 5

Assumptions and limits

The result is derived only from the 2 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 10 decimal places, 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

What is the 5% critical value on 5 df?

11.07, so a statistic of exactly that gives a p value of 0.05.

Why is it right-skewed?

Squares are non-negative and occasionally large, so the distribution has a long right tail that shortens as df grows.