Table 10: Chi-Square Quantiles (Percentiles)
The p-th quantiles (i.e., 100p-th percentiles) of the Chi-Square distribution are tabulated for degrees of freedom m = 1, 2, ...,100. Selected upper-tail quantiles are tabulated here for p = 0.90, 0.95, 0.975, 0.99, 0.995, 0.999, 0.9995. The second part of this table contain selected lower-tail quantiles for p = 0.0005, 0.001, 0.005, 0.01, 0.025, 0.05, 0.10.
Example: The 0.95-th quantile of the Chi-Square distribution with 10 degrees of freedom is 18.30704.
| 100p | |||||||
| m | 90.0 | 95.0 | 97.5 | 99.0 | 99.5 | 99.9 | 99.95 |
| 1 | 2.70554 | 3.84146 | 5.02389 | 6.63490 | 7.87944 | 10.82757 | 12.11567 |
| 2 | 4.60517 | 5.99146 | 7.37776 | 9.21034 | 10.59663 | 13.81551 | 15.20180 |
| 3 | 6.25139 | 7.81473 | 9.34840 | 11.34487 | 12.83816 | 16.26624 | 17.73000 |
| 4 | 7.77944 | 9.48773 | 11.14329 | 13.27670 | 14.86026 | 18.46683 | 19.99736 |
| 5 | 9.23636 | 11.07050 | 12.83250 | 15.08627 | 16.74960 | 20.51501 | 22.10533 |
| 6 | 10.64464 | 12.59159 | 14.44938 | 16.81189 | 18.54758 | 22.45774 | 24.10280 |
| 7 | 12.01704 | 14.06714 | 16.01276 | 18.47531 | 20.27774 | 24.32189 | 26.01777 |
| 8 | 13.36157 | 15.50731 | 17.53455 | 20.09024 | 21.95495 | 26.12448 | 27.86805 |
| 9 | 14.68366 | 16.91898 | 19.02277 | 21.66599 | 23.58935 | 27.87716 | 29.66581 |
| 10 | 15.98718 | 18.30704 | 20.48318 | 23.20925 | 25.18818 | 29.58830 | 31.41981 |
| 11 | 17.27501 | 19.67514 | 21.92005 | 24.72497 | 26.75685 | 31.26413 | 33.13662 |
| 12 | 18.54935 | 21.02607 | 23.33666 | 26.21697 | 28.29952 | 32.90949 | 34.82127 |
| 13 | 19.81193 | 22.36203 | 24.73560 | 27.68825 | 29.81947 | 34.52818 | 36.47779 |
| 14 | 21.06414 | 23.68479 | 26.11895 | 29.14124 | 31.31935 | 36.12327 | 38.10940 |
| 15 | 22.30713 | 24.99579 | 27.48839 | 30.57791 | 32.80132 | 37.69730 | 39.71876 |
| 16 | 23.54183 | 26.29623 | 28.84535 | 31.99993 | 34.26719 | 39.25235 | 41.30807 |
| 17 | 24.76904 | 27.58711 | 30.19101 | 33.40866 | 35.71847 | 40.79022 | 42.87921 |
| 18 | 25.98942 | 28.86930 | 31.52638 | 34.80531 | 37.15645 | 42.31240 | 44.43377 |
| 19 | 27.20357 | 30.14353 | 32.85233 | 36.19087 | 38.58226 | 43.82020 | 45.97312 |
| 20 | 28.41198 | 31.41043 | 34.16961 | 37.56623 | 39.99685 | 45.31475 | 47.49845 |
| 21 | 29.61509 | 32.67057 | 35.47888 | 38.93217 | 41.40106 | 46.79704 | 49.01081 |
| 22 | 30.81328 | 33.92444 | 36.78071 | 40.28936 | 42.79566 | 48.26794 | 50.51112 |
| 23 | 32.00690 | 35.17246 | 38.07563 | 41.63840 | 44.18128 | 49.72823 | 52.00019 |
| 24 | 33.19624 | 36.41503 | 39.36408 | 42.97982 | 45.55851 | 51.17860 | 53.47875 |
| 25 | 34.38159 | 37.65248 | 40.64647 | 44.31410 | 46.92789 | 52.61966 | 54.94746 |
| 26 | 35.56317 | 38.88514 | 41.92317 | 45.64168 | 48.28988 | 54.05196 | 56.40689 |
| 27 | 36.74122 | 40.11327 | 43.19451 | 46.96294 | 49.64492 | 55.47602 | 57.85759 |
| 28 | 37.91592 | 41.33714 | 44.46079 | 48.27824 | 50.99338 | 56.89229 | 59.30003 |
| 29 | 39.08747 | 42.55697 | 45.72229 | 49.58788 | 52.33562 | 58.30117 | 60.73465 |
| 30 | 40.25602 | 43.77297 | 46.97924 | 50.89218 | 53.67196 | 59.70306 | 62.16185 |
| 31 | 41.42174 | 44.98534 | 48.23189 | 52.19139 | 55.00270 | 61.09831 | 63.58201 |
| 32 | 42.58475 | 46.19426 | 49.48044 | 53.48577 | 56.32811 | 62.48722 | 64.99546 |
| 33 | 43.74518 | 47.39988 | 50.72508 | 54.77554 | 57.64845 | 63.87010 | 66.40251 |
| 34 | 44.90316 | 48.60237 | 51.96600 | 56.06091 | 58.96393 | 65.24722 | 67.80346 |
| 35 | 46.05879 | 49.80185 | 53.20335 | 57.34207 | 60.27477 | 66.61883 | 69.19856 |
| 36 | 47.21217 | 50.99846 | 54.43729 | 58.61921 | 61.58118 | 67.98517 | 70.58807 |
| 37 | 48.36341 | 52.19232 | 55.66797 | 59.89250 | 62.88334 | 69.34645 | 71.97222 |
| 38 | 49.51258 | 53.38354 | 56.89552 | 61.16209 | 64.18141 | 70.70289 | 73.35123 |
| 39 | 50.65977 | 54.57223 | 58.12006 | 62.42812 | 65.47557 | 72.05466 | 74.72529 |
| 40 | 51.80506 | 55.75848 | 59.34171 | 63.69074 | 66.76596 | 73.40196 | 76.09460 |
| 41 | 52.94851 | 56.94239 | 60.56057 | 64.95007 | 68.05273 | 74.74494 | 77.45934 |
| 42 | 54.09020 | 58.12404 | 61.77676 | 66.20624 | 69.33600 | 76.08376 | 78.81966 |
| 43 | 55.23019 | 59.30351 | 62.99036 | 67.45935 | 70.61590 | 77.41858 | 80.17573 |
| 44 | 56.36854 | 60.48089 | 64.20146 | 68.70951 | 71.89255 | 78.74952 | 81.52769 |
| 45 | 57.50530 | 61.65623 | 65.41016 | 69.95683 | 73.16606 | 80.07673 | 82.87569 |
| 46 | 58.64054 | 62.82962 | 66.61653 | 71.20140 | 74.43654 | 81.40033 | 84.21985 |
| 47 | 59.77429 | 64.00111 | 67.82065 | 72.44331 | 75.70407 | 82.72042 | 85.56030 |
| 48 | 60.90661 | 65.17077 | 69.02259 | 73.68264 | 76.96877 | 84.03713 | 86.89715 |
| 49 | 62.03754 | 66.33865 | 70.22241 | 74.91947 | 78.23071 | 85.35056 | 88.23052 |
| 50 | 63.16712 | 67.50481 | 71.42020 | 76.15389 | 79.48998 | 86.66082 | 89.56052 |
| 51 | 64.29540 | 68.66929 | 72.61599 | 77.38596 | 80.74666 | 87.96798 | 90.88724 |
| 52 | 65.42241 | 69.83216 | 73.80986 | 78.61576 | 82.00083 | 89.27215 | 92.21078 |
| 53 | 66.54820 | 70.99345 | 75.00186 | 79.84334 | 83.25255 | 90.57341 | 93.53123 |
| 54 | 67.67279 | 72.15322 | 76.19205 | 81.06877 | 84.50190 | 91.87185 | 94.84869 |
| 55 | 68.79621 | 73.31149 | 77.38047 | 82.29212 | 85.74895 | 93.16753 | 96.16322 |
| 56 | 69.91851 | 74.46832 | 78.56716 | 83.51343 | 86.99376 | 94.46054 | 97.47491 |
| 57 | 71.03971 | 75.62375 | 79.75219 | 84.73277 | 88.23638 | 95.75095 | 98.78384 |
| 58 | 72.15984 | 76.77780 | 80.93559 | 85.95018 | 89.47687 | 97.03883 | 100.09008 |
| 59 | 73.27893 | 77.93052 | 82.11741 | 87.16571 | 90.71529 | 98.32423 | 101.39370 |
| 60 | 74.39701 | 79.08194 | 83.29767 | 88.37942 | 91.95170 | 99.60723 | 102.69476 |
| 61 | 75.51409 | 80.23210 | 84.47644 | 89.59134 | 93.18614 | 100.88789 | 103.99332 |
| 62 | 76.63021 | 81.38102 | 85.65373 | 90.80153 | 94.41865 | 102.16625 | 105.28946 |
| 63 | 77.74538 | 82.52873 | 86.82959 | 92.01002 | 95.64930 | 103.44238 | 106.58322 |
| 64 | 78.85964 | 83.67526 | 88.00405 | 93.21686 | 96.87811 | 104.71633 | 107.87467 |
| 65 | 79.97300 | 84.82065 | 89.17715 | 94.42208 | 98.10514 | 105.98814 | 109.16385 |
| 66 | 81.08549 | 85.96491 | 90.34890 | 95.62572 | 99.33043 | 107.25788 | 110.45083 |
| 67 | 82.19711 | 87.10807 | 91.51936 | 96.82782 | 100.55401 | 108.52558 | 111.73564 |
| 68 | 83.30790 | 88.25016 | 92.68854 | 98.02840 | 101.77592 | 109.79130 | 113.01834 |
| 69 | 84.41787 | 89.39121 | 93.85647 | 99.22752 | 102.99621 | 111.05507 | 114.29897 |
| 70 | 85.52704 | 90.53123 | 95.02318 | 100.42518 | 104.21490 | 112.31693 | 115.57758 |
| 71 | 86.63543 | 91.67024 | 96.18870 | 101.62144 | 105.43203 | 113.57694 | 116.85422 |
| 72 | 87.74305 | 92.80827 | 97.35305 | 102.81631 | 106.64763 | 114.83512 | 118.12891 |
| 73 | 88.84992 | 93.94534 | 98.51626 | 104.00983 | 107.86174 | 116.09151 | 119.40172 |
| 74 | 89.95605 | 95.08147 | 99.67835 | 105.20203 | 109.07438 | 117.34616 | 120.67266 |
| 75 | 91.06146 | 96.21667 | 100.83934 | 106.39292 | 110.28558 | 118.59909 | 121.94178 |
| 76 | 92.16617 | 97.35097 | 101.99925 | 107.58254 | 111.49538 | 119.85035 | 123.20912 |
| 77 | 93.27018 | 98.48438 | 103.15811 | 108.77092 | 112.70380 | 121.09996 | 124.47471 |
| 78 | 94.37352 | 99.61693 | 104.31594 | 109.95807 | 113.91087 | 122.34795 | 125.73858 |
| 79 | 95.47619 | 100.74862 | 105.47275 | 111.14402 | 115.11661 | 123.59437 | 127.00077 |
| 80 | 96.57820 | 101.87947 | 106.62857 | 112.32879 | 116.32106 | 124.83922 | 128.26131 |
| 81 | 97.67958 | 103.00951 | 107.78341 | 113.51241 | 117.52422 | 126.08256 | 129.52023 |
| 82 | 98.78033 | 104.13874 | 108.93729 | 114.69489 | 118.72613 | 127.32440 | 130.77756 |
| 83 | 99.88046 | 105.26718 | 110.09024 | 115.87627 | 119.92682 | 128.56477 | 132.03333 |
| 84 | 100.97999 | 106.39484 | 111.24226 | 117.05654 | 121.12629 | 129.80369 | 133.28757 |
| 85 | 102.07892 | 107.52174 | 112.39337 | 118.23575 | 122.32458 | 131.04120 | 134.54030 |
| 86 | 103.17726 | 108.64789 | 113.54360 | 119.41390 | 123.52170 | 132.27732 | 135.79156 |
| 87 | 104.27504 | 109.77331 | 114.69295 | 120.59101 | 124.71768 | 133.51207 | 137.04136 |
| 88 | 105.37225 | 110.89800 | 115.84144 | 121.76711 | 125.91254 | 134.74548 | 138.28973 |
| 89 | 106.46890 | 112.02199 | 116.98908 | 122.94221 | 127.10628 | 135.97757 | 139.53669 |
| 90 | 107.56501 | 113.14527 | 118.13589 | 124.11632 | 128.29894 | 137.20835 | 140.78228 |
| 91 | 108.66058 | 114.26787 | 119.28189 | 125.28946 | 129.49053 | 138.43786 | 142.02651 |
| 92 | 109.75563 | 115.38979 | 120.42708 | 126.46166 | 130.68107 | 139.66612 | 143.26940 |
| 93 | 110.85015 | 116.51105 | 121.57148 | 127.63291 | 131.87058 | 140.89313 | 144.51098 |
| 94 | 111.94417 | 117.63165 | 122.71511 | 128.80325 | 133.05906 | 142.11894 | 145.75127 |
| 95 | 113.03769 | 118.75161 | 123.85797 | 129.97268 | 134.24655 | 143.34354 | 146.99028 |
| 96 | 114.13071 | 119.87094 | 125.00007 | 131.14122 | 135.43305 | 144.56697 | 148.22804 |
| 97 | 115.22324 | 120.98964 | 126.14144 | 132.30888 | 136.61858 | 145.78923 | 149.46457 |
| 98 | 116.31530 | 122.10773 | 127.28207 | 133.47567 | 137.80315 | 147.01036 | 150.69989 |
| 99 | 117.40688 | 123.22522 | 128.42199 | 134.64162 | 138.98678 | 148.23036 | 151.93401 |
| 100 | 118.49800 | 124.34211 | 129.56120 | 135.80672 | 140.16949 | 149.44925 | 153.16696 |
Tabulated by S L C Saw
