Lower (100p)th Percentiles of the Chi-square Distribution 1 p .001 .005 .01 .02 .025 .05 .10 .15 .20 .25 .50 DF 1 0.0000 0.0000 0.0002 0.0006 0.0010 0.0039 0.0158 0.0358 0.0642 0.1015 0.4549 2 0.0020 0.0100 0.0201 0.0404 0.0506 0.1026 0.2107 0.3250 0.4463 0.5754 1.3863 3 0.0243 0.0717 0.1148 0.1848 0.2158 0.3518 0.5844 0.7978 1.0052 1.2125 2.3660 4 0.0908 0.2070 0.2971 0.4294 0.4844 0.7107 1.0636 1.3665 1.6488 1.9226 3.3567 5 0.2102 0.4117 0.5543 0.7519 0.8312 1.1455 1.6103 1.9938 2.3425 2.6746 4.3515 6 0.3811 0.6757 0.8721 1.1344 1.2373 1.6354 2.2041 2.6613 3.0701 3.4546 5.3481 7 0.5985 0.9893 1.2390 1.5643 1.6899 2.1673 2.8331 3.3583 3.8223 4.2549 6.3458 8 0.8571 1.3444 1.6465 2.0325 2.1797 2.7326 3.4895 4.0782 4.5936 5.0706 7.3441 9 1.1519 1.7349 2.0879 2.5324 2.7004 3.3251 4.1682 4.8165 5.3801 5.8988 8.3428 10 1.4787 2.1559 2.5582 3.0591 3.2470 3.9403 4.8652 5.5701 6.1791 6.7372 9.3418 11 1.8339 2.6032 3.0535 3.6087 3.8157 4.5748 5.5778 6.3364 6.9887 7.5841 10.3410 12 2.2142 3.0738 3.5706 4.1783 4.4038 5.2260 6.3038 7.1138 7.8073 8.4384 11.3403 13 2.6172 3.5650 4.1069 4.7654 5.0088 5.8919 7.0415 7.9008 8.6339 9.2991 12.3398 14 3.0407 4.0747 4.6604 5.3682 5.6287 6.5706 7.7895 8.6963 9.4673 10.1653 13.3393 15 3.4827 4.6009 5.2293 5.9849 6.2621 7.2609 8.5468 9.4993 10.3070 11.0365 14.3389 16 3.9416 5.1422 5.8122 6.6142 6.9077 7.9616 9.3122 10.3090 11.1521 11.9122 15.3385 17 4.4161 5.6972 6.4078 7.2550 7.5642 8.6718 10.0852 11.1249 12.0023 12.7919 16.3382 18 4.9048 6.2648 7.0149 7.9062 8.2307 9.3905 10.8649 11.9463 12.8570 13.6753 17.3379 19 5.4068 6.8440 7.6327 8.5670 8.9065 10.1170 11.6509 12.7727 13.7158 14.5620 18.3377 20 5.9210 7.4338 8.2604 9.2367 9.5908 10.8508 12.4426 13.6039 14.5784 15.4518 19.3374 21 6.4467 8.0337 8.8972 9.9146 10.2829 11.5913 13.2396 14.4393 15.4446 16.3444 20.3372 22 6.9830 8.6427 9.5425 10.6000 10.9823 12.3380 14.0415 15.2788 16.3140 17.2396 21.3370 23 7.5292 9.2604 10.1957 11.2926 11.6886 13.0905 14.8480 16.1219 17.1865 18.1373 22.3369 24 8.0849 9.8862 10.8564 11.9918 12.4012 13.8484 15.6587 16.9686 18.0618 19.0373 23.3367 25 8.6493 10.5197 11.5240 12.6973 13.1197 14.6114 16.4734 17.8184 18.9398 19.9393 24.3366 26 9.2221 11.1602 12.1981 13.4086 13.8439 15.3792 17.2919 18.6714 19.8202 20.8434 25.3365 27 9.8028 11.8076 12.8785 14.1254 14.5734 16.1514 18.1139 19.5272 20.7030 21.7494 26.3363 28 10.3909 12.4613 13.5647 14.8475 15.3079 16.9279 18.9392 20.3857 21.5880 22.6572 27.3362 29 10.9861 13.1211 14.2565 15.5745 16.0471 17.7084 19.7677 21.2468 22.4751 23.5666 28.3361 30 11.5880 13.7867 14.9535 16.3062 16.7908 18.4927 20.5992 22.1103 23.3641 24.4776 29.3360 35 14.6878 17.1918 18.5089 20.0274 20.5694 22.4650 24.7967 26.4604 27.8359 29.0540 34.3356 40 17.9164 20.7065 22.1643 23.8376 24.4330 26.5093 29.0505 30.8563 32.3450 33.6603 39.3353 45 21.2507 24.3110 25.9013 27.7203 28.3662 30.6123 33.3504 35.2895 36.8844 38.2910 44.3351 50 24.6739 27.9907 29.7067 31.6639 32.3574 34.7643 37.6886 39.7539 41.4492 42.9421 49.3349 60 31.7383 35.5345 37.4849 39.6994 40.4817 43.1880 46.4589 48.7587 50.6406 52.2938 59.3347 70 39.0364 43.2752 45.4417 47.8934 48.7576 51.7393 55.3289 57.8443 59.8978 61.6983 69.3345 80 46.5199 51.1719 53.5401 56.2128 57.1532 60.3915 64.2778 66.9938 69.2069 71.1445 79.3343 90 54.1552 59.1963 61.7541 64.6347 65.6466 69.1260 73.2911 76.1954 78.5584 80.6247 89.3342 100 61.9179 67.3276 70.0649 73.1422 74.2219 77.9295 82.3581 85.4406 87.9453 90.1332 99.3341 Upper (100p)th Percentiles of the Chi-square Distribution 2 p .001 .005 .01 .02 .025 .05 .10 .15 .20 .25 .50 DF 1 0.4549 1.323 1.642 2.072 2.706 3.841 5.024 5.412 6.635 7.879 10.828 2 1.3863 2.773 3.219 3.794 4.605 5.991 7.378 7.824 9.210 10.597 13.816 3 2.3660 4.108 4.642 5.317 6.251 7.815 9.348 9.837 11.345 12.838 16.266 4 3.3567 5.385 5.989 6.745 7.779 9.488 11.143 11.668 13.277 14.860 18.467 5 4.3515 6.626 7.289 8.115 9.236 11.070 12.833 13.388 15.086 16.750 20.515 6 5.3481 7.841 8.558 9.446 10.645 12.592 14.449 15.033 16.812 18.548 22.458 7 6.3458 9.037 9.803 10.748 12.017 14.067 16.013 16.622 18.475 20.278 24.322 8 7.3441 10.219 11.030 12.027 13.362 15.507 17.535 18.168 20.090 21.955 26.124 9 8.3428 11.389 12.242 13.288 14.684 16.919 19.023 19.679 21.666 23.589 27.877 10 9.3418 12.549 13.442 14.534 15.987 18.307 20.483 21.161 23.209 25.188 29.588 11 10.3410 13.701 14.631 15.767 17.275 19.675 21.920 22.618 24.725 26.757 31.264 12 11.3403 14.845 15.812 16.989 18.549 21.026 23.337 24.054 26.217 28.300 32.909 13 12.3398 15.984 16.985 18.202 19.812 22.362 24.736 25.472 27.688 29.819 34.528 14 13.3393 17.117 18.151 19.406 21.064 23.685 26.119 26.873 29.141 31.319 36.123 15 14.3389 18.245 19.311 20.603 22.307 24.996 27.488 28.259 30.578 32.801 37.697 16 15.3385 19.369 20.465 21.793 23.542 26.296 28.845 29.633 32.000 34.267 39.252 17 16.3382 20.489 21.615 22.977 24.769 27.587 30.191 30.995 33.409 35.718 40.790 18 17.3379 21.605 22.760 24.155 25.989 28.869 31.526 32.346 34.805 37.156 42.312 19 18.3377 22.718 23.900 25.329 27.204 30.144 32.852 33.687 36.191 38.582 43.820 20 19.3374 23.828 25.038 26.498 28.412 31.410 34.170 35.020 37.566 39.997 45.315 21 20.3372 24.935 26.171 27.662 29.615 32.671 35.479 36.343 38.932 41.401 46.797 22 21.3370 26.039 27.301 28.822 30.813 33.924 36.781 37.659 40.289 42.796 48.268 23 22.3369 27.141 28.429 29.979 32.007 35.172 38.076 38.968 41.638 44.181 49.728 24 23.3367 28.241 29.553 31.132 33.196 36.415 39.364 40.270 42.980 45.559 51.179 25 24.3366 29.339 30.675 32.282 34.382 37.652 40.646 41.566 44.314 46.928 52.620 26 25.3365 30.435 31.795 33.429 35.563 38.885 41.923 42.856 45.642 48.290 54.052 27 26.3363 31.528 32.912 34.574 36.741 40.113 43.195 44.140 46.963 49.645 55.476 28 27.3362 32.620 34.027 35.715 37.916 41.337 44.461 45.419 48.278 50.993 56.892 29 28.3361 33.711 35.139 36.854 39.087 42.557 45.722 46.693 49.588 52.336 58.301 30 29.3360 34.800 36.250 37.990 40.256 43.773 46.979 47.962 50.892 53.672 59.703 35 34.3356 40.223 41.778 43.640 46.059 49.802 53.203 54.244 57.342 60.275 66.619 40 39.3353 45.616 47.269 49.244 51.805 55.758 59.342 60.436 63.691 66.766 73.402 45 44.3351 50.985 52.729 54.810 57.505 61.656 65.410 66.555 69.957 73.166 80.077 50 49.3349 56.334 58.164 60.346 63.167 67.505 71.420 72.613 76.154 79.490 86.661 60 59.3347 66.981 68.972 71.341 74.397 79.082 83.298 84.580 88.379 91.952 99.607 70 69.3345 77.577 79.715 82.255 85.527 90.531 95.023 96.388 100.425 104.215 112.317 80 79.3343 88.130 90.405 93.106 96.578 101.879 106.629 108.069 112.329 116.321 124.839 90 89.3342 98.650 101.054 103.904 107.565 113.145 118.136 119.648 124.116 128.299 137.208 100 99.3341 109.141 111.667 114.659 118.498 124.342 129.561 131.142 135.807 140.169 149.449