Upper-tail critical values of chi-square distribution. df Probability less than the critical value 0.90 0.95 0.975 0.99 0.999 1 2.706 3.841 5.024 6.635 10.828 2 4.605 5.991 7.378 9.210 13.816 3 6.251 7.815 9.348 11.345 16.266 4 7.779 9.488 11.143 13.277 18.467 5 9.236 11.070 12.833 15.086 20.515 6 10.645 12.592 14.449 16.812 22.458 7 12.017 14.067 16.013 18.475 24.322 8 13.362 15.507 17.535 20.090 26.125 9 14.684 16.919 19.023 21.666 27.877 10 15.987 18.307 20.483 23.209 29.588 11 17.275 19.675 21.920 24.725 31.264 12 18.549 21.026 23.337 26.217 32.910 13 19.812 22.362 24.736 27.688 34.528 14 21.064 23.685 26.119 29.141 36.123 15 22.307 24.996 27.488 30.578 37.697 16 23.542 26.296 28.845 32.000 39.252 17 24.769 27.587 30.191 33.409 40.790 18 25.989 28.869 31.526 34.805 42.312 19 27.204 30.144 32.852 36.191 43.820 20 28.412 31.410 34.170 37.566 45.315 21 29.615 32.671 35.479 38.932 46.797 22 30.813 33.924 36.781 40.289 48.268 23 32.007 35.172 38.076 41.638 49.728 24 33.196 36.415 39.364 42.980 51.179 25 34.382 37.652 40.646 44.314 52.620 26 35.563 38.885 41.923 45.642 54.052 27 36.741 40.113 43.195 46.963 55.476 28 37.916 41.337 44.461 48.278 56.892 29 39.087 42.557 45.722 49.588 58.301 30 40.256 43.773 46.979 50.892 59.703 31 41.422 44.985 48.232 52.191 61.098 32 42.585 46.194 49.480 53.486 62.487 33 43.745 47.400 50.725 54.776 63.870 34 44.903 48.602 51.966 56.061 65.247 35 46.059 49.802 53.203 57.342 66.619 36 47.212 50.998 54.437 58.619 67.985 37 48.363 52.192 55.668 59.893 69.347 38 49.513 53.384 56.896 61.162 70.703 39 50.660 54.572 58.120 62.428 72.055 40 51.805 55.758 59.342 63.691 73.402 41 52.949 56.942 60.561 64.950 74.745 42 54.090 58.124 61.777 66.206 76.084 43 55.230 59.304 62.990 67.459 77.419 44 56.369 60.481 64.201 68.710 78.750 45 57.505 61.656 65.410 69.957 80.077 46 58.641 62.830 66.617 71.201 81.400 47 59.774 64.001 67.821 72.443 82.720 48 60.907 65.171 69.023 73.683 84.037 49 62.038 66.339 70.222 74.919 85.351 50 63.167 67.505 71.420 76.154 86.661 51 64.295 68.669 72.616 77.386 87.968 52 65.422 69.832 73.810 78.616 89.272 53 66.548 70.993 75.002 79.843 90.573 54 67.673 72.153 76.192 81.069 91.872 55 68.796 73.311 77.380 82.292 93.168 56 69.919 74.468 78.567 83.513 94.461 57 71.040 75.624 79.752 84.733 95.751 58 72.160 76.778 80.936 85.950 97.039 59 73.279 77.931 82.117 87.166 98.324 60 74.397 79.082 83.298 88.379 99.607 61 75.514 80.232 84.476 89.591 100.888 62 76.630 81.381 85.654 90.802 102.166 63 77.745 82.529 86.830 92.010 103.442 64 78.860 83.675 88.004 93.217 104.716 65 79.973 84.821 89.177 94.422 105.988 66 81.085 85.965 90.349 95.626 107.258 67 82.197 87.108 91.519 96.828 108.526 68 83.308 88.250 92.689 98.028 109.791 69 84.418 89.391 93.856 99.228 111.055 70 85.527 90.531 95.023 100.425 112.317 71 86.635 91.670 96.189 101.621 113.577 72 87.743 92.808 97.353 102.816 114.835 73 88.850 93.945 98.516 104.010 116.092 74 89.956 95.081 99.678 105.202 117.346 75 91.061 96.217 100.839 106.393 118.599 76 92.166 97.351 101.999 107.583 119.850 77 93.270 98.484 103.158 108.771 121.100 78 94.374 99.617 104.316 109.958 122.348 79 95.476 100.749 105.473 111.144 123.594 80 96.578 101.879 106.629 112.329 124.839 81 97.680 103.010 107.783 113.512 126.083 82 98.780 104.139 108.937 114.695 127.324 83 99.880 105.267 110.090 115.876 128.565 84 100.980 106.395 111.242 117.057 129.804 85 102.079 107.522 112.393 118.236 131.041 86 103.177 108.648 113.544 119.414 132.277 87 104.275 109.773 114.693 120.591 133.512 88 105.372 110.898 115.841 121.767 134.746 89 106.469 112.022 116.989 122.942 135.978 90 107.565 113.145 118.136 124.116 137.208 91 108.661 114.268 119.282 125.289 138.438 92 109.756 115.390 120.427 126.462 139.666 93 110.850 116.511 121.571 127.633 140.893 94 111.944 117.632 122.715 128.803 142.119 95 113.038 118.752 123.858 129.973 143.344 96 114.131 119.871 125.000 131.141 144.567 97 115.223 120.990 126.141 132.309 145.789 98 116.315 122.108 127.282 133.476 147.010 99 117.407 123.225 128.422 134.642 148.230 100 118.498 124.342 129.561 135.807 149.449