The percentage points table of the Chi-Square distribution lists numbers called critical values ranging from 0.1 % to 99.9 %. The value v represents degree of freedom, i.e., the total number of free parameters being tested in a statistical comparison. This table depicts the chi square percentage points from 0.1 to 50 %.
Chi Square Percentage Values from 0.1 to 50.0 %
| v | 0.1% | 0.5% | 1.0% | 2.5% | 5.0% | 10.0% | 12.5% | 20.0% | 25.0% | 33.3% | 50.0% |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.000 | 0.000 | 0.000 | 0.001 | 0.004 | 0.016 | 0.025 | 0.064 | 0.102 | 0.186 | 0.455 |
| 2 | 0.002 | 0.010 | 0.020 | 0.051 | 0.103 | 0.211 | 0.267 | 0.446 | 0.575 | 0.811 | 1.386 |
| 3 | 0.024 | 0.072 | 0.115 | 0.216 | 0.352 | 0.584 | 0.692 | 1.005 | 1.213 | 1.568 | 2.366 |
| 4 | 0.091 | 0.207 | 0.297 | 0.484 | 0.711 | 1.064 | 1.219 | 1.649 | 1.923 | 2.378 | 3.357 |
| 5 | 0.210 | 0.412 | 0.554 | 0.831 | 1.145 | 1.610 | 1.808 | 2.343 | 2.675 | 3.216 | 4.351 |
| 6 | 0.381 | 0.676 | 0.872 | 1.237 | 1.635 | 2.204 | 2.441 | 3.070 | 3.455 | 4.074 | 5.348 |
| 7 | 0.598 | 0.989 | 1.239 | 1.690 | 2.167 | 2.833 | 3.106 | 3.822 | 4.255 | 4.945 | 6.346 |
| 8 | 0.857 | 1.344 | 1.646 | 2.180 | 2.733 | 3.490 | 3.797 | 4.594 | 5.071 | 5.826 | 7.344 |
| 9 | 1.152 | 1.735 | 2.088 | 2.700 | 3.325 | 4.168 | 4.507 | 5.380 | 5.899 | 6.716 | 8.343 |
| 10 | 1.479 | 2.156 | 2.558 | 3.247 | 3.940 | 4.865 | 5.234 | 6.179 | 6.737 | 7.612 | 9.342 |
| 11 | 1.834 | 2.603 | 3.053 | 3.816 | 4.575 | 5.578 | 5.975 | 6.989 | 7.584 | 8.514 | 10.341 |
| 12 | 2.214 | 3.074 | 3.571 | 4.404 | 5.226 | 6.304 | 6.729 | 7.807 | 8.438 | 9.420 | 11.340 |
| 13 | 2.617 | 3.565 | 4.107 | 5.009 | 5.892 | 7.042 | 7.493 | 8.634 | 9.299 | 10.331 | 12.340 |
| 14 | 3.041 | 4.075 | 4.660 | 5.629 | 6.571 | 7.790 | 8.266 | 9.467 | 10.165 | 11.245 | 13.339 |
| 15 | 3.483 | 4.601 | 5.229 | 6.262 | 7.261 | 8.547 | 9.048 | 10.307 | 11.037 | 12.163 | 14.339 |
| 16 | 3.942 | 5.142 | 5.812 | 6.908 | 7.962 | 9.312 | 9.837 | 11.152 | 11.912 | 13.083 | 15.338 |
| 17 | 4.416 | 5.697 | 6.408 | 7.564 | 8.672 | 10.085 | 10.633 | 12.002 | 12.792 | 14.006 | 16.338 |
| 18 | 4.905 | 6.265 | 7.015 | 8.231 | 9.390 | 10.865 | 11.435 | 12.857 | 13.675 | 14.931 | 17.338 |
| 19 | 5.407 | 6.844 | 7.633 | 8.907 | 10.117 | 11.651 | 12.242 | 13.716 | 14.562 | 15.859 | 18.338 |
| 20 | 5.921 | 7.434 | 8.260 | 9.591 | 10.851 | 12.443 | 13.055 | 14.578 | 15.452 | 16.788 | 19.337 |
| 21 | 6.447 | 8.034 | 8.897 | 10.283 | 11.591 | 13.240 | 13.873 | 15.445 | 16.344 | 17.720 | 20.337 |
| 22 | 6.983 | 8.643 | 9.542 | 10.982 | 12.338 | 14.041 | 14.695 | 16.314 | 17.240 | 18.653 | 21.337 |
| 23 | 7.529 | 9.260 | 10.196 | 11.689 | 13.091 | 14.848 | 15.521 | 17.187 | 18.137 | 19.587 | 22.337 |
| 24 | 8.085 | 9.886 | 10.856 | 12.401 | 13.848 | 15.659 | 16.351 | 18.062 | 19.037 | 20.523 | 23.337 |
| 25 | 8.649 | 10.520 | 11.524 | 13.120 | 14.611 | 16.473 | 17.184 | 18.940 | 19.939 | 21.461 | 24.337 |
| 26 | 9.222 | 11.160 | 12.198 | 13.844 | 15.379 | 17.292 | 18.021 | 19.820 | 20.843 | 22.399 | 25.336 |
| 27 | 9.803 | 11.808 | 12.879 | 14.573 | 16.151 | 18.114 | 18.861 | 20.703 | 21.749 | 23.339 | 26.336 |
| 28 | 10.391 | 12.461 | 13.565 | 15.308 | 16.928 | 18.939 | 19.704 | 21.588 | 22.657 | 24.280 | 27.336 |
| 29 | 10.986 | 13.121 | 14.256 | 16.047 | 17.708 | 19.768 | 20.550 | 22.475 | 23.567 | 25.222 | 28.336 |
| 30 | 11.588 | 13.787 | 14.953 | 16.791 | 18.493 | 20.599 | 21.399 | 23.364 | 24.478 | 26.165 | 29.336 |
| 35 | 14.688 | 17.192 | 18.509 | 20.569 | 22.465 | 24.797 | 25.678 | 27.836 | 29.054 | 30.894 | 34.336 |
| 40 | 17.916 | 20.707 | 22.164 | 24.433 | 26.509 | 29.051 | 30.008 | 32.345 | 33.660 | 35.643 | 39.335 |
| 45 | 21.251 | 24.311 | 25.901 | 28.366 | 30.612 | 33.350 | 34.379 | 36.884 | 38.291 | 40.407 | 44.335 |
| 50 | 24.674 | 27.991 | 29.707 | 32.357 | 34.764 | 37.689 | 38.785 | 41.449 | 42.942 | 45.184 | 49.335 |
| 55 | 28.173 | 31.735 | 33.570 | 36.398 | 38.958 | 42.060 | 43.220 | 46.036 | 47.610 | 49.972 | 54.335 |
| 60 | 31.738 | 35.534 | 37.485 | 40.482 | 43.188 | 46.459 | 47.680 | 50.641 | 52.294 | 54.770 | 59.3351 |
Chi Square Percentage Values from 60.0 % to 99.9 %
| v | 60.0% | 66.7% | 75.0% | 80.0% | 87.5% | 90.0% | 95.0% | 97.5% | 99.0% | 99.5% | 99.9% |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.708 | 0.936 | 1.323 | 1.642 | 2.354 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
| 2 | 1.833 | 2.197 | 2.773 | 3.219 | 4.159 | 4.605 | 5.991 | 7.378 | 9.210 | 10.597 | 13.816 |
| 3 | 2.946 | 3.405 | 4.108 | 4.642 | 5.739 | 6.251 | 7.815 | 9.348 | 11.345 | 12.838 | 16.266 |
| 4 | 4.045 | 4.579 | 5.385 | 5.989 | 7.214 | 7.779 | 9.488 | 11.143 | 13.277 | 14.860 | 18.467 |
| 5 | 5.132 | 5.730 | 6.626 | 7.289 | 8.625 | 9.236 | 11.070 | 12.833 | 15.086 | 16.750 | 20.515 |
| 6 | 6.211 | 6.867 | 7.841 | 8.558 | 9.992 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 | 22.458 |
| 7 | 7.283 | 7.992 | 9.037 | 9.803 | 11.326 | 12.017 | 14.067 | 16.013 | 18.475 | 20.278 | 24.322 |
| 8 | 8.351 | 9.107 | 10.219 | 11.030 | 12.636 | 13.362 | 15.507 | 17.535 | 20.090 | 21.955 | 26.125 |
| 9 | 9.414 | 10.215 | 11.389 | 12.242 | 13.926 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 | 27.877 |
| 10 | 10.473 | 11.317 | 12.549 | 13.442 | 15.198 | 15.987 | 18.307 | 20.483 | 23.209 | 25.188 | 29.588 |
| 11 | 11.530 | 12.414 | 13.701 | 14.631 | 16.457 | 17.275 | 19.675 | 21.920 | 24.725 | 26.757 | 31.264 |
| 12 | 12.584 | 13.506 | 14.845 | 15.812 | 17.703 | 18.549 | 21.026 | 23.337 | 26.217 | 28.300 | 32.910 |
| 13 | 13.636 | 14.595 | 15.984 | 16.985 | 18.939 | 19.812 | 22.362 | 24.736 | 27.688 | 29.819 | 34.528 |
| 14 | 14.685 | 15.680 | 17.117 | 18.151 | 20.166 | 21.064 | 23.685 | 26.119 | 29.141 | 31.319 | 36.123 |
| 15 | 15.733 | 16.761 | 18.245 | 19.311 | 21.384 | 22.307 | 24.996 | 27.488 | 30.578 | 32.801 | 37.697 |
| 16 | 16.780 | 17.840 | 19.369 | 20.465 | 22.595 | 23.542 | 26.296 | 28.845 | 32.000 | 34.267 | 39.252 |
| 17 | 17.824 | 18.917 | 20.489 | 21.615 | 23.799 | 24.769 | 27.587 | 30.191 | 33.409 | 35.718 | 40.790 |
| 18 | 18.868 | 19.991 | 21.605 | 22.760 | 24.997 | 25.989 | 28.869 | 31.526 | 34.805 | 37.156 | 42.312 |
| 19 | 19.910 | 21.063 | 22.718 | 23.900 | 26.189 | 27.204 | 30.144 | 32.852 | 36.191 | 38.582 | 43.820 |
| 20 | 20.951 | 22.133 | 23.828 | 25.038 | 27.376 | 28.412 | 31.410 | 34.170 | 37.566 | 39.997 | 45.315 |
| 21 | 21.991 | 23.201 | 24.935 | 26.171 | 28.559 | 29.615 | 32.671 | 35.479 | 38.932 | 41.401 | 46.797 |
| 22 | 23.031 | 24.268 | 26.039 | 27.301 | 29.737 | 30.813 | 33.924 | 36.781 | 40.289 | 42.796 | 48.268 |
| 23 | 24.069 | 25.333 | 27.141 | 28.429 | 30.911 | 32.007 | 35.172 | 38.076 | 41.638 | 44.181 | 49.728 |
| 24 | 25.106 | 26.397 | 28.241 | 29.553 | 32.081 | 33.196 | 36.415 | 39.364 | 42.9804 | 5.559 | 51.179 |
| 25 | 26.143 | 27.459 | 29.339 | 30.675 | 33.247 | 34.382 | 37.652 | 40.646 | 44.314 | 46.928 | 52.620 |
| 26 | 27.179 | 28.520 | 30.435 | 31.795 | 34.410 | 35.563 | 38.885 | 41.923 | 45.642 | 48.290 | 54.052 |
| 27 | 28.214 | 29.580 | 31.528 | 32.912 | 35.570 | 36.741 | 40.113 | 43.195 | 46.963 | 49.645 | 55.476 |
| 28 | 29.249 | 30.639 | 32.620 | 34.027 | 36.727 | 37.916 | 41.337 | 44.461 | 48.278 | 50.993 | 56.892 |
| 29 | 30.283 | 31.697 | 33.711 | 35.139 | 37.881 | 39.087 | 42.557 | 45.722 | 49.588 | 52.336 | 58.301 |
| 30 | 31.316 | 32.754 | 34.800 | 36.250 | 39.033 | 40.256 | 43.773 | 46.979 | 50.892 | 53.672 | 59.703 |
| 35 | 36.475 | 38.024 | 40.223 | 41.778 | 44.753 | 46.059 | 49.802 | 53.203 | 57.342 | 60.275 | 66.619 |
| 40 | 41.622 | 43.275 | 45.616 | 47.269 | 50.424 | 51.805 | 55.758 | 59.342 | 63.691 | 66.766 | 73.402 |
| 45 | 46.761 | 48.510 | 50.985 | 52.729 | 56.052 | 57.505 | 61.656 | 65.410 | 69.957 | 73.166 | 80.077 |
| 50 | 51.892 | 53.733 | 56.334 | 58.164 | 61.647 | 63.167 | 67.505 | 71.420 | 76.154 | 79.490 | 86.661 |
| 55 | 57.016 | 58.945 | 61.665 | 63.577 | 67.211 | 68.796 | 73.311 | 77.380 | 82.292 | 85.749 | 93.168 |
| 60 | 62.135 | 64.147 | 66.981 | 68.972 | 72.751 | 74.397 | 79.082 | 83.298 | 88.379 | 91.952 | 99.6072 |
