Engineering Tables/Chi-Squared Distribution

Table of values of χ2 in a Chi-Squared Distribution with k degrees of freedom such that p is the area between χ2 and +∞Image:Chi-Squared_Distribution_Diagram.svgkProbability Content, p, between χ2 and +∞0.9950.990.9750.950.90.750.50.250.10.050.0250.010.0050.0020.0011 3.927e-5 1.570e-4 9.820e-4 0.00393 0.0157 0.102 0.455 1.323 2.706 3.841 5.024 6.635 7.879 9.550 10.8282 0.0100 0.0201 0.0506 0.103 0.211 0.575 1.386 2.773 4.605 5.991 7.378 9.210 10.597 12.429 13.8163 0.0717 0.115 0.216 0.352 0.584 1.213 2.366 4.108 6.251 7.815 9.348 11.345 12.838 14.796 16.2664 0.207 0.297 0.484 0.711 1.064 1.923 3.357 5.385 7.779 9.488 11.143 13.277 14.860 16.924 18.4675 0.412 0.554 0.831 1.145 1.610 2.675 4.351 6.626 9.236 11.070 12.833 15.086 16.750 18.907 20.5156 0.676 0.872 1.237 1.635 2.204 3.455 5.348 7.841 10.645 12.592 14.449 16.812 18.548 20.791 22.4587 0.989 1.239 1.690 2.167 2.833 4.255 6.346 9.037 12.017 14.067 16.013 18.475 20.278 22.601 24.3228 1.344 1.646 2.180 2.733 3.490 5.071 7.344 10.219 13.362 15.507 17.535 20.090 21.955 24.352 26.1249 1.735 2.088 2.700 3.325 4.168 5.899 8.343 11.389 14.684 16.919 19.023 21.666 23.589 26.056 27.87710 2.156 2.558 3.247 3.940 4.865 6.737 9.342 12.549 15.987 18.307 20.483 23.209 25.188 27.722 29.58811 2.603 3.053 3.816 4.575 5.578 7.584 10.341 13.701 17.275 19.675 21.920 24.725 26.757 29.354 31.26412 3.074 3.571 4.404 5.226 6.304 8.438 11.340 14.845 18.549 21.026 23.337 26.217 28.300 30.957 32.90913 3.565 4.107 5.009 5.892 7.042 9.299 12.340 15.984 19.812 22.362 24.736 27.688 29.819 32.535 34.52814 4.075 4.660 5.629 6.571 7.790 10.165 13.339 17.117 21.064 23.685 26.119 29.141 31.319 34.091 36.12315 4.601 5.229 6.262 7.261 8.547 11.037 14.339 18.245 22.307 24.996 27.488 30.578 32.801 35.628 37.69716 5.142 5.812 6.908 7.962 9.312 11.912 15.338 19.369 23.542 26.296 28.845 32.000 34.267 37.146 39.25217 5.697 6.408 7.564 8.672 10.085 12.792 16.338 20.489 24.769 27.587 30.191 33.409 35.718 38.648 40.79018 6.265 7.015 8.231 9.390 10.865 13.675 17.338 21.605 25.989 28.869 31.526 34.805 37.156 40.136 42.31219 6.844 7.633 8.907 10.117 11.651 14.562 18.338 22.718 27.204 30.144 32.852 36.191 38.582 41.610 43.82020 7.434 8.260 9.591 10.851 12.443 15.452 19.337 23.828 28.412 31.410 34.170 37.566 39.997 43.072 45.31521 8.034 8.897 10.283 11.591 13.240 16.344 20.337 24.935 29.615 32.671 35.479 38.932 41.401 44.522 46.79722 8.643 9.542 10.982 12.338 14.041 17.240 21.337 26.039 30.813 33.924 36.781 40.289 42.796 45.962 48.26823 9.260 10.196 11.689 13.091 14.848 18.137 22.337 27.141 32.007 35.172 38.076 41.638 44.181 47.391 49.72824 9.886 10.856 12.401 13.848 15.659 19.037 23.337 28.241 33.196 36.415 39.364 42.980 45.559 48.812 51.17925 10.520 11.524 13.120 14.611 16.473 19.939 24.337 29.339 34.382 37.652 40.646 44.314 46.928 50.223 52.62026 11.160 12.198 13.844 15.379 17.292 20.843 25.336 30.435 35.563 38.885 41.923 45.642 48.290 51.627 54.05227 11.808 12.879 14.573 16.151 18.114 21.749 26.336 31.528 36.741 40.113 43.195 46.963 49.645 53.023 55.47628 12.461 13.565 15.308 16.928 18.939 22.657 27.336 32.620 37.916 41.337 44.461 48.278 50.993 54.411 56.89229 13.121 14.256 16.047 17.708 19.768 23.567 28.336 33.711 39.087 42.557 45.722 49.588 52.336 55.792 58.30130 13.787 14.953 16.791 18.493 20.599 24.478 29.336 34.800 40.256 43.773 46.979 50.892 53.672 57.167 59.70331 14.458 15.655 17.539 19.281 21.434 25.390 30.336 35.887 41.422 44.985 48.232 52.191 55.003 58.536 61.09832 15.134 16.362 18.291 20.072 22.271 26.304 31.336 36.973 42.585 46.194 49.480 53.486 56.328 59.899 62.48733 15.815 17.074 19.047 20.867 23.110 27.219 32.336 38.058 43.745 47.400 50.725 54.776 57.648 61.256 63.87034 16.501 17.789 19.806 21.664 23.952 28.136 33.336 39.141 44.903 48.602 51.966 56.061 58.964 62.608 65.24735 17.192 18.509 20.569 22.465 24.797 29.054 34.336 40.223 46.059 49.802 53.203 57.342 60.275 63.955 66.61936 17.887 19.233 21.336 23.269 25.643 29.973 35.336 41.304 47.212 50.998 54.437 58.619 61.581 65.296 67.98537 18.586 19.960 22.106 24.075 26.492 30.893 36.336 42.383 48.363 52.192 55.668 59.893 62.883 66.633 69.34638 19.289 20.691 22.878 24.884 27.343 31.815 37.335 43.462 49.513 53.384 56.896 61.162 64.181 67.966 70.70339 19.996 21.426 23.654 25.695 28.196 32.737 38.335 44.539 50.660 54.572 58.120 62.428 65.476 69.294 72.05540 20.707 22.164 24.433 26.509 29.051 33.660 39.335 45.616 51.805 55.758 59.342 63.691 66.766 70.618 73.40241 21.421 22.906 25.215 27.326 29.907 34.585 40.335 46.692 52.949 56.942 60.561 64.950 68.053 71.938 74.74542 22.138 23.650 25.999 28.144 30.765 35.510 41.335 47.766 54.090 58.124 61.777 66.206 69.336 73.254 76.08443 22.859 24.398 26.785 28.965 31.625 36.436 42.335 48.840 55.230 59.304 62.990 67.459 70.616 74.566 77.41944 23.584 25.148 27.575 29.787 32.487 37.363 43.335 49.913 56.369 60.481 64.201 68.710 71.893 75.874 78.75045 24.311 25.901 28.366 30.612 33.350 38.291 44.335 50.985 57.505 61.656 65.410 69.957 73.166 77.179 80.07746 25.041 26.657 29.160 31.439 34.215 39.220 45.335 52.056 58.641 62.830 66.617 71.201 74.437 78.481 81.40047 25.775 27.416 29.956 32.268 35.081 40.149 46.335 53.127 59.774 64.001 67.821 72.443 75.704 79.780 82.72048 26.511 28.177 30.755 33.098 35.949 41.079 47.335 54.196 60.907 65.171 69.023 73.683 76.969 81.075 84.03749 27.249 28.941 31.555 33.930 36.818 42.010 48.335 55.265 62.038 66.339 70.222 74.919 78.231 82.367 85.35150 27.991 29.707 32.357 34.764 37.689 42.942 49.335 56.334 63.167 67.505 71.420 76.154 79.490 83.657 86.66151 28.735 30.475 33.162 35.600 38.560 43.874 50.335 57.401 64.295 68.669 72.616 77.386 80.747 84.943 87.96852 29.481 31.246 33.968 36.437 39.433 44.808 51.335 58.468 65.422 69.832 73.810 78.616 82.001 86.227 89.27253 30.230 32.018 34.776 37.276 40.308 45.741 52.335 59.534 66.548 70.993 75.002 79.843 83.253 87.507 90.57354 30.981 32.793 35.586 38.116 41.183 46.676 53.335 60.600 67.673 72.153 76.192 81.069 84.502 88.786 91.87255 31.735 33.570 36.398 38.958 42.060 47.610 54.335 61.665 68.796 73.311 77.380 82.292 85.749 90.061 93.16856 32.490 34.350 37.212 39.801 42.937 48.546 55.335 62.729 69.919 74.468 78.567 83.513 86.994 91.335 94.46157 33.248 35.131 38.027 40.646 43.816 49.482 56.335 63.793 71.040 75.624 79.752 84.733 88.236 92.605 95.75158 34.008 35.913 38.844 41.492 44.696 50.419 57.335 64.857 72.160 76.778 80.936 85.950 89.477 93.874 97.03959 34.770 36.698 39.662 42.339 45.577 51.356 58.335 65.919 73.279 77.931 82.117 87.166 90.715 95.140 98.32460 35.534 37.485 40.482 43.188 46.459 52.294 59.335 66.981 74.397 79.082 83.298 88.379 91.952 96.404 99.60761 36.301 38.273 41.303 44.038 47.342 53.232 60.335 68.043 75.514 80.232 84.476 89.591 93.186 97.665100.88862 37.068 39.063 42.126 44.889 48.226 54.171 61.335 69.104 76.630 81.381 85.654 90.802 94.419 98.925102.16663 37.838 39.855 42.950 45.741 49.111 55.110 62.335 70.165 77.745 82.529 86.830 92.010 95.649100.182103.44264 38.610 40.649 43.776 46.595 49.996 56.050 63.335 71.225 78.860 83.675 88.004 93.217 96.878101.437104.71665 39.383 41.444 44.603 47.450 50.883 56.990 64.335 72.285 79.973 84.821 89.177 94.422 98.105102.691105.98866 40.158 42.240 45.431 48.305 51.770 57.931 65.335 73.344 81.085 85.965 90.349 95.626 99.330103.942107.25867 40.935 43.038 46.261 49.162 52.659 58.872 66.335 74.403 82.197 87.108 91.519 96.828100.554105.192108.52668 41.713 43.838 47.092 50.020 53.548 59.814 67.335 75.461 83.308 88.250 92.689 98.028101.776106.440109.79169 42.494 44.639 47.924 50.879 54.438 60.756 68.334 76.519 84.418 89.391 93.856 99.228102.996107.685111.05570 43.275 45.442 48.758 51.739 55.329 61.698 69.334 77.577 85.527 90.531 95.023100.425104.215108.929112.31771 44.058 46.246 49.592 52.600 56.221 62.641 70.334 78.634 86.635 91.670 96.189101.621105.432110.172113.57772 44.843 47.051 50.428 53.462 57.113 63.585 71.334 79.690 87.743 92.808 97.353102.816106.648111.412114.83573 45.629 47.858 51.265 54.325 58.006 64.528 72.334 80.747 88.850 93.945 98.516104.010107.862112.651116.09274 46.417 48.666 52.103 55.189 58.900 65.472 73.334 81.803 89.956 95.081 99.678105.202109.074113.889117.34675 47.206 49.475 52.942 56.054 59.795 66.417 74.334 82.858 91.061 96.217100.839106.393110.286115.125118.59976 47.997 50.286 53.782 56.920 60.690 67.362 75.334 83.913 92.166 97.351101.999107.583111.495116.359119.85077 48.788 51.097 54.623 57.786 61.586 68.307 76.334 84.968 93.270 98.484103.158108.771112.704117.591121.10078 49.582 51.910 55.466 58.654 62.483 69.252 77.334 86.022 94.374 99.617104.316109.958113.911118.823122.34879 50.376 52.725 56.309 59.522 63.380 70.198 78.334 87.077 95.476100.749105.473111.144115.117120.052123.59480 51.172 53.540 57.153 60.391 64.278 71.145 79.334 88.130 96.578101.879106.629112.329116.321121.280124.83981 51.969 54.357 57.998 61.261 65.176 72.091 80.334 89.184 97.680103.010107.783113.512117.524122.507126.08382 52.767 55.174 58.845 62.132 66.076 73.038 81.334 90.237 98.780104.139108.937114.695118.726123.733127.32483 53.567 55.993 59.692 63.004 66.976 73.985 82.334 91.289 99.880105.267110.090115.876119.927124.957128.56584 54.368 56.813 60.540 63.876 67.876 74.933 83.334 92.342100.980106.395111.242117.057121.126126.179129.80485 55.170 57.634 61.389 64.749 68.777 75.881 84.334 93.394102.079107.522112.393118.236122.325127.401131.04186 55.973 58.456 62.239 65.623 69.679 76.829 85.334 94.446103.177108.648113.544119.414123.522128.621132.27787 56.777 59.279 63.089 66.498 70.581 77.777 86.334 95.497104.275109.773114.693120.591124.718129.840133.51288 57.582 60.103 63.941 67.373 71.484 78.726 87.334 96.548105.372110.898115.841121.767125.913131.057134.74589 58.389 60.928 64.793 68.249 72.387 79.675 88.334 97.599106.469112.022116.989122.942127.106132.273135.97890 59.196 61.754 65.647 69.126 73.291 80.625 89.334 98.650107.565113.145118.136124.116128.299133.489137.20891 60.005 62.581 66.501 70.003 74.196 81.574 90.334 99.700108.661114.268119.282125.289129.491134.702138.43892 60.815 63.409 67.356 70.882 75.100 82.524 91.334100.750109.756115.390120.427126.462130.681135.915139.66693 61.625 64.238 68.211 71.760 76.006 83.474 92.334101.800110.850116.511121.571127.633131.871137.127140.89394 62.437 65.068 69.068 72.640 76.912 84.425 93.334102.850111.944117.632122.715128.803133.059138.337142.11995 63.250 65.898 69.925 73.520 77.818 85.376 94.334103.899113.038118.752123.858129.973134.247139.546143.34496 64.063 66.730 70.783 74.401 78.725 86.327 95.334104.948114.131119.871125.000131.141135.433140.755144.56797 64.878 67.562 71.642 75.282 79.633 87.278 96.334105.997115.223120.990126.141132.309136.619141.962145.78998 65.694 68.396 72.501 76.164 80.541 88.229 97.334107.045116.315122.108127.282133.476137.803143.168147.01099 66.510 69.230 73.361 77.046 81.449 89.181 98.334108.093117.407123.225128.422134.642138.987144.373148.230100 67.328 70.065 74.222 77.929 82.358 90.133 99.334109.141118.498124.342129.561135.807140.169145.577149.449101 68.146 70.901 75.083 78.813 83.267 91.085100.334110.189119.589125.458130.700136.971141.351146.780150.667102 68.965 71.737 75.946 79.697 84.177 92.038101.334111.236120.679126.574131.838138.134142.532147.982151.884103 69.785 72.575 76.809 80.582 85.088 92.991102.334112.284121.769127.689132.975139.297143.712149.183153.099104 70.606 73.413 77.672 81.468 85.998 93.944103.334113.331122.858128.804134.111140.459144.891150.383154.314105 71.428 74.252 78.536 82.354 86.909 94.897104.334114.378123.947129.918135.247141.620146.070151.582155.528106 72.251 75.092 79.401 83.240 87.821 95.850105.334115.424125.035131.031136.382142.780147.247152.780156.740107 73.075 75.932 80.267 84.127 88.733 96.804106.334116.471126.123132.144137.517143.940148.424153.977157.952108 73.899 76.774 81.133 85.015 89.645 97.758107.334117.517127.211133.257138.651145.099149.599155.173159.162109 74.724 77.616 82.000 85.903 90.558 98.712108.334118.563128.298134.369139.784146.257150.774156.369160.372110 75.550 78.458 82.867 86.792 91.471 99.666109.334119.608129.385135.480140.917147.414151.948157.563161.581111 76.377 79.302 83.735 87.681 92.385100.620110.334120.654130.472136.591142.049148.571153.122158.757162.788112 77.204 80.146 84.604 88.570 93.299101.575111.334121.699131.558137.701143.180149.727154.294159.950163.995113 78.033 80.991 85.473 89.461 94.213102.530112.334122.744132.643138.811144.311150.882155.466161.141165.201114 78.862 81.836 86.342 90.351 95.128103.485113.334123.789133.729139.921145.441152.037156.637162.332166.406115 79.692 82.682 87.213 91.242 96.043104.440114.334124.834134.813141.030146.571153.191157.808163.523167.610116 80.522 83.529 88.084 92.134 96.958105.396115.334125.878135.898142.138147.700154.344158.977164.712168.813117 81.353 84.377 88.955 93.026 97.874106.352116.334126.923136.982143.246148.829155.496160.146165.900170.016118 82.185 85.225 89.827 93.918 98.790107.307117.334127.967138.066144.354149.957156.648161.314167.088171.217119 83.018 86.074 90.700 94.811 99.707108.263118.334129.011139.149145.461151.084157.800162.481168.275172.418120 83.852 86.923 91.573 95.705100.624109.220119.334130.055140.233146.567152.211158.950163.648169.461173.617121 84.686 87.773 92.446 96.598101.541110.176120.334131.098141.315147.674153.338160.100164.814170.647174.816122 85.520 88.624 93.320 97.493102.458111.133121.334132.142142.398148.779154.464161.250165.980171.831176.014123 86.356 89.475 94.195 98.387103.376112.089122.334133.185143.480149.885155.589162.398167.144173.015177.212124 87.192 90.327 95.070 99.283104.295113.046123.334134.228144.562150.989156.714163.546168.308174.198178.408125 88.029 91.180 95.946100.178105.213114.004124.334135.271145.643152.094157.839164.694169.471175.380179.604126 88.866 92.033 96.822101.074106.132114.961125.334136.313146.724153.198158.962165.841170.634176.562180.799127 89.704 92.887 97.698101.971107.051115.918126.334137.356147.805154.302160.086166.987171.796177.743181.993128 90.543 93.741 98.576102.867107.971116.876127.334138.398148.885155.405161.209168.133172.957178.923183.186129 91.382 94.596 99.453103.765108.891117.834128.334139.440149.965156.508162.331169.278174.118180.103184.379130 92.222 95.451100.331104.662109.811118.792129.334140.482151.045157.610163.453170.423175.278181.282185.571131 93.063 96.307101.210105.560110.732119.750130.334141.524152.125158.712164.575171.567176.438182.460186.762132 93.904 97.163102.089106.459111.652120.708131.334142.566153.204159.814165.696172.711177.597183.637187.953133 94.746 98.020102.968107.357112.573121.667132.334143.608154.283160.915166.816173.854178.755184.814189.142134 95.588 98.878103.848108.257113.495122.625133.334144.649155.361162.016167.936174.996179.913185.990190.331135 96.431 99.736104.729109.156114.417123.584134.334145.690156.440163.116169.056176.138181.070187.165191.520136 97.275100.595105.609110.056115.338124.543135.334146.731157.518164.216170.175177.280182.226188.340192.707137 98.119101.454106.491110.956116.261125.502136.334147.772158.595165.316171.294178.421183.382189.514193.894138 98.964102.314107.372111.857117.183126.461137.334148.813159.673166.415172.412179.561184.538190.688195.080139 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