Table of the (non-central) $\chi^2$ distribution



Let $X \sim \chi^2_k = \chi^2(k)$, $k$ = # degrees of freedom \[ f(x;k) = \left\{\begin{array}{ll} \frac{x^{\frac{k}{2} - 1}e^{-\frac{x}{2}}}{2^\frac{k}{2}~\Gamma(\frac{k}{2})} & x \geq 0 \\ 0 & \text{, otherwise} \\ \end{array} \right. \] $P(X \leq x)$ is given by: \[ \int_{0}^x f(x;k)dx \]



$\chi^2_{0.995}$ $\chi^2_{0.99}$ $\chi^2_{0.975}$ $\chi^2_{0.95}$ $\chi^2_{0.9}$ $\chi^2_{0.75}$ $\chi^2_{0.5}$ $\chi^2_{0.25}$ $\chi^2_{0.1}$ $\chi^2_{0.05}$ $\chi^2_{0.01}$
1 7.9 6.6 5.0 3.8 2.7 1.3 0.5 0.1 0.0 0.0 0.0
2 10.6 9.2 7.4 6.0 4.6 2.8 1.4 0.6 0.2 0.1 0.0
3 12.8 11.3 9.3 7.8 6.3 4.1 2.4 1.2 0.6 0.4 0.1
4 14.9 13.3 11.1 9.5 7.8 5.4 3.4 1.9 1.1 0.7 0.3
5 16.7 15.1 12.8 11.1 9.2 6.6 4.4 2.7 1.6 1.1 0.6
6 18.5 16.8 14.4 12.6 10.6 7.8 5.3 3.5 2.2 1.6 0.9
7 20.3 18.5 16.0 14.1 12.0 9.0 6.3 4.3 2.8 2.2 1.2
8 22.0 20.1 17.5 15.5 13.4 10.2 7.3 5.1 3.5 2.7 1.6
9 23.6 21.7 19.0 16.9 14.7 11.4 8.3 5.9 4.2 3.3 2.1
10 25.2 23.2 20.5 18.3 16.0 12.5 9.3 6.7 4.9 3.9 2.6
11 26.8 24.7 21.9 19.7 17.3 13.7 10.3 7.6 5.6 4.6 3.1
12 28.3 26.2 23.3 21.0 18.5 14.8 11.3 8.4 6.3 5.2 3.6
13 29.8 27.7 24.7 22.4 19.8 16.0 12.3 9.3 7.0 5.9 4.1
14 31.3 29.1 26.1 23.7 21.1 17.1 13.3 10.2 7.8 6.6 4.7
15 32.8 30.6 27.5 25.0 22.3 18.2 14.3 11.0 8.5 7.3 5.2
16 34.3 32.0 28.8 26.3 23.5 19.4 15.3 11.9 9.3 8.0 5.8
17 35.7 33.4 30.2 27.6 24.8 20.5 16.3 12.8 10.1 8.7 6.4
18 37.2 34.8 31.5 28.9 26.0 21.6 17.3 13.7 10.9 9.4 7.0
19 38.6 36.2 32.9 30.1 27.2 22.7 18.3 14.6 11.7 10.1 7.6
20 40.0 37.6 34.2 31.4 28.4 23.8 19.3 15.5 12.4 10.9 8.3
21 41.4 38.9 35.5 32.7 29.6 24.9 20.3 16.3 13.2 11.6 8.9
22 42.8 40.3 36.8 33.9 30.8 26.0 21.3 17.2 14.0 12.3 9.5
23 44.2 41.6 38.1 35.2 32.0 27.1 22.3 18.1 14.8 13.1 10.2
24 45.6 43.0 39.4 36.4 33.2 28.2 23.3 19.0 15.7 13.8 10.9
25 46.9 44.3 40.6 37.7 34.4 29.3 24.3 19.9 16.5 14.6 11.5
26 48.3 45.6 41.9 38.9 35.6 30.4 25.3 20.8 17.3 15.4 12.2
27 49.6 47.0 43.2 40.1 36.7 31.5 26.3 21.7 18.1 16.2 12.9
28 51.0 48.3 44.5 41.3 37.9 32.6 27.3 22.7 18.9 16.9 13.6
29 52.3 49.6 45.7 42.6 39.1 33.7 28.3 23.6 19.8 17.7 14.3
30 53.7 50.9 47.0 43.8 40.3 34.8 29.3 24.5 20.6 18.5 15.0
40 66.8 63.7 59.3 55.8 51.8 45.6 39.3 33.7 29.1 26.5 22.2
50 79.5 76.2 71.4 67.5 63.2 56.3 49.3 42.9 37.7 34.8 29.7
60 92.0 88.4 83.3 79.1 74.4 67.0 59.3 52.3 46.5 43.2 37.5
70 104.2 100.4 95.0 90.5 85.5 77.6 69.3 61.7 55.3 51.7 45.4