Chi-square distribution table
From OPOSSEM
The following table consists of critical values of the chi-square (χ²) distribution for selected confidence levels (90%, 95%, and 99%) between 1 and 100 degrees of freedom. To use this table, identify the column with the appropriate confidence level and then find the row with the number of degrees of freedom appropriate for the statistical test; for example, in the chi-square test of association for two-way tables, <math>\text{df} = (r-1)\times(c-1)</math> where r and c are the number of rows and columns in the table, respectively.
df | 90% | 95% | 99% |
---|---|---|---|
1 | 2.706 | 3.841 | 6.635 |
2 | 4.605 | 5.991 | 9.210 |
3 | 6.251 | 7.815 | 11.345 |
4 | 7.779 | 9.488 | 13.277 |
5 | 9.236 | 11.070 | 15.086 |
6 | 10.645 | 12.592 | 16.812 |
7 | 12.017 | 14.067 | 18.475 |
8 | 13.362 | 15.507 | 20.090 |
9 | 14.684 | 16.919 | 21.666 |
10 | 15.987 | 18.307 | 23.209 |
11 | 17.275 | 19.675 | 24.725 |
12 | 18.549 | 21.026 | 26.217 |
13 | 19.812 | 22.362 | 27.688 |
14 | 21.064 | 23.685 | 29.141 |
15 | 22.307 | 24.996 | 30.578 |
16 | 23.542 | 26.296 | 32.000 |
17 | 24.769 | 27.587 | 33.409 |
18 | 25.989 | 28.869 | 34.805 |
19 | 27.204 | 30.144 | 36.191 |
20 | 28.412 | 31.410 | 37.566 |
21 | 29.615 | 32.671 | 38.932 |
22 | 30.813 | 33.924 | 40.289 |
23 | 32.007 | 35.172 | 41.638 |
24 | 33.196 | 36.415 | 42.980 |
25 | 34.382 | 37.652 | 44.314 |
26 | 35.563 | 38.885 | 45.642 |
27 | 36.741 | 40.113 | 46.963 |
28 | 37.916 | 41.337 | 48.278 |
29 | 39.087 | 42.557 | 49.588 |
30 | 40.256 | 43.773 | 50.892 |
31 | 41.422 | 44.985 | 52.191 |
32 | 42.585 | 46.194 | 53.486 |
33 | 43.745 | 47.400 | 54.776 |
34 | 44.903 | 48.602 | 56.061 |
35 | 46.059 | 49.802 | 57.342 |
36 | 47.212 | 50.998 | 58.619 |
37 | 48.363 | 52.192 | 59.893 |
38 | 49.513 | 53.384 | 61.162 |
39 | 50.660 | 54.572 | 62.428 |
40 | 51.805 | 55.758 | 63.691 |
41 | 52.949 | 56.942 | 64.950 |
42 | 54.090 | 58.124 | 66.206 |
43 | 55.230 | 59.304 | 67.459 |
44 | 56.369 | 60.481 | 68.710 |
45 | 57.505 | 61.656 | 69.957 |
46 | 58.641 | 62.830 | 71.201 |
47 | 59.774 | 64.001 | 72.443 |
48 | 60.907 | 65.171 | 73.683 |
49 | 62.038 | 66.339 | 74.919 |
50 | 63.167 | 67.505 | 76.154 |
51 | 64.295 | 68.669 | 77.386 |
52 | 65.422 | 69.832 | 78.616 |
53 | 66.548 | 70.993 | 79.843 |
54 | 67.673 | 72.153 | 81.069 |
55 | 68.796 | 73.311 | 82.292 |
56 | 69.919 | 74.468 | 83.513 |
57 | 71.040 | 75.624 | 84.733 |
58 | 72.160 | 76.778 | 85.950 |
59 | 73.279 | 77.931 | 87.166 |
60 | 74.397 | 79.082 | 88.379 |
61 | 75.514 | 80.232 | 89.591 |
62 | 76.630 | 81.381 | 90.802 |
63 | 77.745 | 82.529 | 92.010 |
64 | 78.860 | 83.675 | 93.217 |
65 | 79.973 | 84.821 | 94.422 |
66 | 81.085 | 85.965 | 95.626 |
67 | 82.197 | 87.108 | 96.828 |
68 | 83.308 | 88.250 | 98.028 |
69 | 84.418 | 89.391 | 99.228 |
70 | 85.527 | 90.531 | 100.425 |
71 | 86.635 | 91.670 | 101.621 |
72 | 87.743 | 92.808 | 102.816 |
73 | 88.850 | 93.945 | 104.010 |
74 | 89.956 | 95.081 | 105.202 |
75 | 91.061 | 96.217 | 106.393 |
76 | 92.166 | 97.351 | 107.583 |
77 | 93.270 | 98.484 | 108.771 |
78 | 94.374 | 99.617 | 109.958 |
79 | 95.476 | 100.749 | 111.144 |
80 | 96.578 | 101.879 | 112.329 |
81 | 97.680 | 103.010 | 113.512 |
82 | 98.780 | 104.139 | 114.695 |
83 | 99.880 | 105.267 | 115.876 |
84 | 100.980 | 106.395 | 117.057 |
85 | 102.079 | 107.522 | 118.236 |
86 | 103.177 | 108.648 | 119.414 |
87 | 104.275 | 109.773 | 120.591 |
88 | 105.372 | 110.898 | 121.767 |
89 | 106.469 | 112.022 | 122.942 |
90 | 107.565 | 113.145 | 124.116 |
91 | 108.661 | 114.268 | 125.289 |
92 | 109.756 | 115.390 | 126.462 |
93 | 110.850 | 116.511 | 127.633 |
94 | 111.944 | 117.632 | 128.803 |
95 | 113.038 | 118.752 | 129.973 |
96 | 114.131 | 119.871 | 131.141 |
97 | 115.223 | 120.990 | 132.309 |
98 | 116.315 | 122.108 | 133.476 |
99 | 117.407 | 123.225 | 134.642 |
100 | 118.498 | 124.342 | 135.807 |