Chi-Square Distribution

The Chi-square distribution is defined by:

f(x) = {1/[2n/2* G(n/2)]} * [x(n/2)-1 * e-x/2]

n = 1, 2, ...

x > 0



is the degrees of freedom


is the base of the natural logarithm, sometimes called Euler's e (2.71...)

G (gamma)

is the Gamma function

The above animation shows the shape of the Chi-square distribution as the degrees of freedom increase (1, 2, 5, 10, 25 and 50). Note that optimum scaling (rather than fixed scaling) is used in the animation (see Probability Distribution Calculator for further details). For a complete listing of all distribution functions, see Distributions and Their Functions.