Percentile Points of the Chi-Square Distribution
Click on the desired degrees of freedom:
1 - 10 | 11 - 20 | 21 - 30 | 31 - 40 | 41 - 50 |
51 - 60 | 61 - 70 | 71 - 80 | 81 - 90 | 91 - 100 |
Degrees of Freedom 1 - 10
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
1 | 2.706 | 3.841 | 5.412 | 6.635 | 9.550 | 10.828 |
2 | 4.605 | 5.991 | 7.824 | 9.210 | 12.429 | 13.816 |
3 | 6.251 | 7.815 | 9.837 | 11.345 | 14.796 | 16.267 |
4 | 7.779 | 9.488 | 11.668 | 13.277 | 16.924 | 18.467 |
5 | 9.236 | 11.071 | 13.388 | 15.086 | 18.908 | 20.516 |
6 | 10.645 | 12.592 | 15.033 | 16.812 | 20.791 | 22.458 |
7 | 12.017 | 14.067 | 16.622 | 18.475 | 22.601 | 24.323 |
8 | 13.362 | 15.507 | 18.168 | 20.090 | 24.352 | 26.125 |
9 | 14.684 | 16.919 | 19.679 | 21.666 | 26.057 | 27.878 |
10 | 15.987 | 18.307 | 21.161 | 23.209 | 27.722 | 29.589 |
Degrees of Freedom 11 - 20
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
11 | 17.275 | 19.675 | 22.618 | 24.725 | 29.354 | 31.265 |
12 | 18.549 | 21.026 | 24.054 | 26.217 | 30.957 | 32.911 |
13 | 19.812 | 22.362 | 25.472 | 27.688 | 32.536 | 34.530 |
14 | 21.064 | 23.685 | 26.873 | 29.141 | 34.092 | 36.125 |
15 | 22.307 | 24.996 | 28.260 | 30.578 | 35.628 | 37.698 |
16 | 23.542 | 26.296 | 29.633 | 32.000 | 37.147 | 39.254 |
17 | 24.769 | 27.587 | 30.995 | 33.409 | 38.649 | 40.792 |
18 | 25.989 | 28.869 | 32.346 | 34.805 | 40.137 | 42.314 |
19 | 27.204 | 30.144 | 33.687 | 36.191 | 41.611 | 43.822 |
20 | 28.412 | 31.410 | 35.020 | 37.566 | 43.073 | 45.316 |
Degrees of Freedom 21 - 30
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
21 | 29.615 | 32.671 | 36.344 | 38.932 | 44.523 | 46.800 |
22 | 30.813 | 33.924 | 37.660 | 40.290 | 45.963 | 48.270 |
23 | 32.007 | 35.172 | 38.968 | 41.639 | 47.392 | 49.730 |
24 | 33.196 | 36.415 | 40.270 | 42.980 | 48.813 | 51.181 |
25 | 34.382 | 37.653 | 41.566 | 44.314 | 50.224 | 52.621 |
26 | 35.563 | 38.885 | 42.856 | 45.642 | 51.628 | 54.054 |
27 | 36.741 | 40.113 | 44.140 | 46.963 | 53.024 | 55.478 |
28 | 37.916 | 41.337 | 45.419 | 48.278 | 54.413 | 56.895 |
29 | 39.087 | 42.557 | 46.693 | 49.588 | 55.794 | 58.303 |
30 | 40.256 | 43.773 | 47.962 | 50.892 | 57.169 | 59.706 |
Degrees of Freedom 31 - 40
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
31 | 41.422 | 44.985 | 49.227 | 52.192 | 58.537 | 61.100 |
32 | 42.585 | 46.194 | 50.487 | 53.486 | 59.901 | 62.490 |
33 | 43.745 | 47.400 | 51.743 | 54.776 | 61.257 | 63.872 |
34 | 44.903 | 48.602 | 52.995 | 56.061 | 62.610 | 65.250 |
35 | 46.059 | 49.802 | 54.244 | 57.342 | 63.956 | 66.621 |
36 | 47.212 | 50.999 | 55.489 | 58.620 | 65.298 | 67.988 |
37 | 48.363 | 52.192 | 56.731 | 59.893 | 66.634 | 69.350 |
38 | 49.513 | 53.384 | 57.969 | 61.162 | 67.967 | 70.706 |
39 | 50.660 | 54.572 | 59.204 | 62.428 | 69.296 | 72.058 |
40 | 51.805 | 55.759 | 60.436 | 63.691 | 70.619 | 73.405 |
Degrees of Freedom 41 - 50
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
41 | 52.949 | 56.942 | 61.666 | 64.951 | 71.939 | 74.748 |
42 | 54.090 | 58.124 | 62.892 | 66.207 | 73.255 | 76.086 |
43 | 55.230 | 59.304 | 64.116 | 67.460 | 74.567 | 77.422 |
44 | 56.369 | 60.481 | 65.337 | 68.710 | 75.877 | 78.754 |
45 | 57.505 | 61.656 | 66.555 | 69.957 | 77.181 | 80.080 |
46 | 58.641 | 62.830 | 67.772 | 71.202 | 78.483 | 81.404 |
47 | 59.774 | 64.001 | 68.985 | 72.444 | 79.781 | 82.723 |
48 | 60.907 | 65.171 | 70.197 | 73.683 | 81.077 | 84.041 |
49 | 62.038 | 66.339 | 71.406 | 74.920 | 82.370 | 85.355 |
50 | 63.167 | 67.505 | 72.613 | 76.154 | 83.658 | 86.664 |
Degrees of Freedom 51 - 60
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
51 | 64.295 | 68.669 | 73.819 | 77.386 | 84.945 | 87.972 |
52 | 65.422 | 69.832 | 75.022 | 78.616 | 86.229 | 89.277 |
53 | 66.548 | 70.994 | 76.223 | 79.844 | 87.509 | 90.577 |
54 | 67.673 | 72.153 | 77.422 | 81.069 | 88.788 | 91.876 |
55 | 68.796 | 73.312 | 78.619 | 82.293 | 90.064 | 93.171 |
56 | 69.919 | 74.468 | 79.815 | 83.514 | 91.336 | 94.464 |
57 | 71.040 | 75.624 | 81.009 | 84.733 | 92.608 | 95.756 |
58 | 72.160 | 76.778 | 82.201 | 85.951 | 93.875 | 97.042 |
59 | 73.279 | 77.931 | 83.391 | 87.166 | 95.142 | 98.328 |
60 | 74.397 | 79.082 | 84.580 | 88.380 | 96.406 | 99.612 |
Degrees of Freedom 61 - 70
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
61 | 75.514 | 80.232 | 85.767 | 89.592 | 97.667 | 100.892 |
62 | 76.630 | 81.381 | 86.953 | 90.802 | 98.927 | 102.171 |
63 | 77.745 | 82.529 | 88.137 | 92.010 | 100.185 | 103.448 |
64 | 78.860 | 83.675 | 89.320 | 93.217 | 101.439 | 104.720 |
65 | 79.973 | 84.821 | 90.501 | 94.423 | 102.693 | 105.993 |
66 | 81.086 | 85.965 | 91.681 | 95.626 | 103.945 | 107.264 |
67 | 82.197 | 87.108 | 92.860 | 96.828 | 105.195 | 108.530 |
68 | 83.308 | 88.250 | 94.037 | 98.029 | 106.442 | 109.796 |
69 | 84.418 | 89.391 | 95.213 | 99.228 | 107.688 | 111.061 |
70 | 85.527 | 90.531 | 96.388 | 100.426 | 108.933 | 112.321 |
Degrees of Freedom 71 - 80
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
71 | 86.636 | 91.670 | 97.561 | 101.622 | 110.174 | 113.582 |
72 | 87.743 | 92.808 | 98.733 | 102.817 | 111.415 | 114.841 |
73 | 88.850 | 93.945 | 99.904 | 104.010 | 112.655 | 116.096 |
74 | 89.956 | 95.082 | 101.074 | 105.203 | 113.891 | 117.351 |
75 | 91.062 | 96.217 | 102.243 | 106.394 | 115.127 | 118.605 |
76 | 92.166 | 97.351 | 103.410 | 107.583 | 116.362 | 119.857 |
77 | 93.270 | 98.485 | 104.577 | 108.771 | 117.595 | 121.105 |
78 | 94.374 | 99.617 | 105.742 | 109.959 | 118.825 | 122.354 |
79 | 95.476 | 100.749 | 106.906 | 111.145 | 120.055 | 123.601 |
80 | 96.578 | 101.880 | 108.070 | 112.329 | 121.284 | 124.844 |
Degrees of Freedom 81 - 90
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
81 | 97.680 | 103.010 | 109.232 | 113.513 | 122.510 | 126.088 |
82 | 98.780 | 104.139 | 110.393 | 114.696 | 123.736 | 127.331 |
83 | 99.881 | 105.267 | 111.553 | 115.877 | 124.960 | 128.569 |
84 | 100.980 | 106.395 | 112.713 | 117.057 | 126.182 | 129.809 |
85 | 102.079 | 107.522 | 113.871 | 118.236 | 127.404 | 131.048 |
86 | 103.177 | 108.648 | 115.028 | 119.415 | 128.624 | 132.285 |
87 | 104.275 | 109.773 | 116.185 | 120.592 | 129.843 | 133.517 |
88 | 105.372 | 110.898 | 117.340 | 121.768 | 131.060 | 134.752 |
89 | 106.469 | 112.022 | 118.495 | 122.943 | 132.276 | 135.985 |
90 | 107.565 | 113.145 | 119.649 | 124.117 | 133.492 | 137.213 |
Degrees of Freedom 91 - 100
of Freedom |
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0.100 | 0.050 | 0.020 | 0.010 | 0.002 | 0.001 | |
91 | 108.661 | 114.268 | 120.802 | 125.290 | 134.707 | 138.444 |
92 | 109.756 | 115.390 | 121.954 | 126.462 | 135.918 | 139.673 |
93 | 110.850 | 116.511 | 123.105 | 127.634 | 137.130 | 140.901 |
94 | 111.944 | 117.632 | 124.256 | 128.804 | 138.341 | 142.124 |
95 | 113.038 | 118.752 | 125.405 | 129.974 | 139.549 | 143.350 |
96 | 114.131 | 119.871 | 126.554 | 131.142 | 140.758 | 144.574 |
97 | 115.223 | 120.990 | 127.702 | 132.310 | 141.965 | 145.798 |
98 | 116.315 | 122.108 | 128.850 | 133.477 | 143.172 | 147.016 |
99 | 117.407 | 123.225 | 129.996 | 134.643 | 144.376 | 148.237 |
100 | 118.498 | 124.342 | 131.142 | 135.807 | 145.580 | 149.457 |
These values are based on an algorithm developed by D.J. Best and D.E. Roberts as published in P. Griffiths and I.D. Hill's Applied Statistical Algorithms (1986) Ellis Horwood Limited: Chichester, England