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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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

Degrees
of
Freedom
Alpha Level
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