Upper critical values of the F distribution
for numerator degrees of
freedom and denominator degrees of freedom
5% significance level
\ 1 2 3 4 5 6 7 8 9 10
1. 161.448 18.513 10.128 7.709 6.608 5.987 5.591 5.318 5.117 4.965
2. 199.500 19.000 9.552 6.944 5.786 5.143 4.737 4.459 4.256 4.103
3. 215.707 19.164 9.277 6.591 5.409 4.757 4.347 4.066 3.863 3.708
4. 224.583 19.247 9.117 6.388 5.192 4.534 4.120 3.838 3.633 3.478
5. 230.162 19.296 9.013 6.256 5.050 4.387 3.972 3.687 3.482 3.326
6. 233.986 19.330 8.941 6.163 4.950 4.284 3.866 3.581 3.374 3.217
7. 236.768 19.353 8.887 6.094 4.876 4.207 3.787 3.500 3.293 3.135
8. 238.882 19.371 8.845 6.041 4.818 4.147 3.726 3.438 3.230 3.072
9. 240.543 19.385 8.812 5.999 4.772 4.099 3.677 3.388 3.179 3.020
10. 241.882 19.396 8.786 5.964 4.735 4.060 3.637 3.347 3.137 2.978
11. 242.983 19.405 8.763 5.936 4.704 4.027 3.603 3.313 3.102 2.943
12. 243.906 19.413 8.745 5.912 4.678 4.000 3.575 3.284 3.073 2.913
13. 244.690 19.419 8.729 5.891 4.655 3.976 3.550 3.259 3.048 2.887
14. 245.364 19.424 8.715 5.873 4.636 3.956 3.529 3.237 3.025 2.865
15. 245.950 19.429 8.703 5.858 4.619 3.938 3.511 3.218 3.006 2.845
16. 246.464 19.433 8.692 5.844 4.604 3.922 3.494 3.202 2.989 2.828
17. 246.918 19.437 8.683 5.832 4.590 3.908 3.480 3.187 2.974 2.812
18. 247.323 19.440 8.675 5.821 4.579 3.896 3.467 3.173 2.960 2.798
19. 247.686 19.443 8.667 5.811 4.568 3.884 3.455 3.161 2.948 2.785
20. 248.013 19.446 8.660 5.803 4.558 3.874 3.445 3.150 2.936 2.774
21. 248.310 19.448 8.654 5.795 4.549 3.865 3.435 3.140 2.926 2.764
22. 248.579 19.450 8.648 5.787 4.541 3.856 3.426 3.131 2.917 2.754
23. 248.826 19.452 8.643 5.781 4.534 3.849 3.418 3.123 2.908 2.745
24. 249.052 19.454 8.639 5.774 4.527 3.841 3.410 3.115 2.900 2.737
25. 249.260 19.456 8.634 5.769 4.521 3.835 3.404 3.108 2.893 2.730
26. 249.452 19.457 8.630 5.763 4.515 3.829 3.397 3.102 2.886 2.723
27. 249.631 19.459 8.626 5.759 4.510 3.823 3.391 3.095 2.880 2.716
28. 249.797 19.460 8.623 5.754 4.505 3.818 3.386 3.090 2.874 2.710
29. 249.951 19.461 8.620 5.750 4.500 3.813 3.381 3.084 2.869 2.705
30. 250.095 19.462 8.617 5.746 4.496 3.808 3.376 3.079 2.864 2.700
31. 250.230 19.463 8.614 5.742 4.492 3.804 3.371 3.075 2.859 2.695
32. 250.357 19.464 8.611 5.739 4.488 3.800 3.367 3.070 2.854 2.690
33. 250.476 19.465 8.609 5.735 4.484 3.796 3.363 3.066 2.850 2.686
34. 250.588 19.466 8.606 5.732 4.481 3.792 3.359 3.062 2.846 2.681
35. 250.693 19.467 8.604 5.729 4.478 3.789 3.356 3.059 2.842 2.678
36. 250.793 19.468 8.602 5.727 4.474 3.786 3.352 3.055 2.839 2.674
37. 250.888 19.469 8.600 5.724 4.472 3.783 3.349 3.052 2.835 2.670
38. 250.977 19.469 8.598 5.722 4.469 3.780 3.346 3.049 2.832 2.667
39. 251.062 19.470 8.596 5.719 4.466 3.777 3.343 3.046 2.829 2.664
40. 251.143 19.471 8.594 5.717 4.464 3.774 3.340 3.043 2.826 2.661
41. 251.220 19.471 8.593 5.715 4.461 3.772 3.338 3.040 2.823 2.658
42. 251.293 19.472 8.591 5.713 4.459 3.769 3.335 3.037 2.820 2.655
43. 251.363 19.472 8.590 5.711 4.457 3.767 3.333 3.035 2.818 2.653
44. 251.430 19.473 8.588 5.709 4.455 3.765 3.331 3.033 2.815 2.650
45. 251.493 19.474 8.587 5.707 4.453 3.763 3.328 3.030 2.813 2.648
46. 251.554 19.474 8.586 5.706 4.451 3.761 3.326 3.028 2.811 2.645
47. 251.613 19.474 8.584 5.704 4.449 3.759 3.324 3.026 2.809 2.643
48. 251.669 19.475 8.583 5.702 4.448 3.757 3.322 3.024 2.807 2.641
49. 251.723 19.475 8.582 5.701 4.446 3.755 3.321 3.022 2.805 2.639
50. 251.774 19.476 8.581 5.699 4.444 3.754 3.319 3.020 2.803 2.637
51. 251.823 19.476 8.580 5.698 4.443 3.752 3.317 3.019 2.801 2.635
52. 251.871 19.476 8.579 5.697 4.441 3.750 3.316 3.017 2.799 2.633
53. 251.917 19.477 8.578 5.696 4.440 3.749 3.314 3.015 2.798 2.632
54. 251.961 19.477 8.577 5.694 4.439 3.748 3.312 3.014 2.796 2.630
55. 252.004 19.478 8.576 5.693 4.437 3.746 3.311 3.012 2.794 2.628
56. 252.045 19.478 8.575 5.692 4.436 3.745 3.310 3.011 2.793 2.627
57. 252.085 19.478 8.574 5.691 4.435 3.743 3.308 3.009 2.791 2.625
58. 252.123 19.478 8.574 5.690 4.434 3.742 3.307 3.008 2.790 2.624
59. 252.160 19.479 8.573 5.689 4.432 3.741 3.306 3.007 2.789 2.622
60. 252.196 19.479 8.572 5.688 4.431 3.740 3.304 3.005 2.787 2.621
61. 252.230 19.479 8.571 5.687 4.430 3.739 3.303 3.004 2.786 2.620
62. 252.264 19.480 8.571 5.686 4.429 3.738 3.302 3.003 2.785 2.618
63. 252.296 19.480 8.570 5.685 4.428 3.736 3.301 3.002 2.784 2.617
64. 252.327 19.480 8.569 5.684 4.427 3.735 3.300 3.001 2.782 2.616
65. 252.358 19.480 8.569 5.683 4.426 3.734 3.299 2.999 2.781 2.615
66. 252.387 19.481 8.568 5.682 4.425 3.733 3.298 2.998 2.780 2.614
67. 252.416 19.481 8.567 5.682 4.425 3.733 3.297 2.997 2.779 2.613
68. 252.444 19.481 8.567 5.681 4.424 3.732 3.296 2.996 2.778 2.612
69. 252.471 19.481 8.566 5.680 4.423 3.731 3.295 2.995 2.777 2.611
70. 252.497 19.481 8.566 5.679 4.422 3.730 3.294 2.994 2.776 2.610
71. 252.523 19.482 8.565 5.679 4.421 3.729 3.293 2.994 2.775 2.609
72. 252.547 19.482 8.564 5.678 4.420 3.728 3.292 2.993 2.774 2.608
73. 252.571 19.482 8.564 5.677 4.420 3.727 3.291 2.992 2.773 2.607
74. 252.595 19.482 8.563 5.677 4.419 3.727 3.290 2.991 2.772 2.606
75. 252.618 19.482 8.563 5.676 4.418 3.726 3.290 2.990 2.771 2.605
76. 252.640 19.483 8.562 5.675 4.418 3.725 3.289 2.989 2.771 2.604
77. 252.662 19.483 8.562 5.675 4.417 3.724 3.288 2.988 2.770 2.603
78. 252.683 19.483 8.562 5.674 4.416 3.724 3.287 2.988 2.769 2.602
79. 252.703 19.483 8.561 5.674 4.416 3.723 3.287 2.987 2.768 2.602
80. 252.723 19.483 8.561 5.673 4.415 3.722 3.286 2.986 2.768 2.601
81. 252.743 19.483 8.560 5.672 4.414 3.722 3.285 2.986 2.767 2.600
82. 252.763 19.484 8.560 5.672 4.414 3.721 3.285 2.985 2.766 2.599
83. 252.781 19.484 8.559 5.671 4.413 3.720 3.284 2.984 2.765 2.599
84. 252.799 19.484 8.559 5.671 4.413 3.720 3.283 2.983 2.765 2.598
85. 252.817 19.484 8.559 5.670 4.412 3.719 3.283 2.983 2.764 2.597
86. 252.835 19.484 8.558 5.670 4.412 3.719 3.282 2.982 2.763 2.596
87. 252.851 19.484 8.558 5.669 4.411 3.718 3.282 2.982 2.763 2.596
88. 252.868 19.484 8.558 5.669 4.410 3.718 3.281 2.981 2.762 2.595
89. 252.884 19.484 8.557 5.668 4.410 3.717 3.280 2.980 2.761 2.595
90. 252.900 19.485 8.557 5.668 4.409 3.716 3.280 2.980 2.761 2.594
91. 252.915 19.485 8.557 5.668 4.409 3.716 3.279 2.979 2.760 2.593
92. 252.931 19.485 8.556 5.667 4.409 3.715 3.279 2.979 2.760 2.593
93. 252.945 19.485 8.556 5.667 4.408 3.715 3.278 2.978 2.759 2.592
94. 252.960 19.485 8.556 5.666 4.408 3.714 3.278 2.978 2.759 2.592
95. 252.974 19.485 8.555 5.666 4.407 3.714 3.277 2.977 2.758 2.591
96. 252.988 19.485 8.555 5.666 4.407 3.714 3.277 2.977 2.758 2.590
97. 253.002 19.485 8.555 5.665 4.406 3.713 3.276 2.976 2.757 2.590
98. 253.015 19.486 8.554 5.665 4.406 3.713 3.276 2.976 2.757 2.589
99. 253.028 19.486 8.554 5.664 4.405 3.712 3.275 2.975 2.756 2.589
100. 253.041 19.486 8.554 5.664 4.405 3.712 3.275 2.975 2.756 2.588
\ 11 12 13 14 15 16 17 18 19 20
1. 4.844 4.747 4.667 4.600 4.543 4.494 4.451 4.414 4.381 4.351
2. 3.982 3.885 3.806 3.739 3.682 3.634 3.592 3.555 3.522 3.493
3. 3.587 3.490 3.411 3.344 3.287 3.239 3.197 3.160 3.127 3.098
4. 3.357 3.259 3.179 3.112 3.056 3.007 2.965 2.928 2.895 2.866
5. 3.204 3.106 3.025 2.958 2.901 2.852 2.810 2.773 2.740 2.711
6. 3.095 2.996 2.915 2.848 2.790 2.741 2.699 2.661 2.628 2.599
7. 3.012 2.913 2.832 2.764 2.707 2.657 2.614 2.577 2.544 2.514
8. 2.948 2.849 2.767 2.699 2.641 2.591 2.548 2.510 2.477 2.447
9. 2.896 2.796 2.714 2.646 2.588 2.538 2.494 2.456 2.423 2.393
10. 2.854 2.753 2.671 2.602 2.544 2.494 2.450 2.412 2.378 2.348
11. 2.818 2.717 2.635 2.565 2.507 2.456 2.413 2.374 2.340 2.310
12. 2.788 2.687 2.604 2.534 2.475 2.425 2.381 2.342 2.308 2.278
13. 2.761 2.660 2.577 2.507 2.448 2.397 2.353 2.314 2.280 2.250
14. 2.739 2.637 2.554 2.484 2.424 2.373 2.329 2.290 2.256 2.225
15. 2.719 2.617 2.533 2.463 2.403 2.352 2.308 2.269 2.234 2.203
16. 2.701 2.599 2.515 2.445 2.385 2.333 2.289 2.250 2.215 2.184
17. 2.685 2.583 2.499 2.428 2.368 2.317 2.272 2.233 2.198 2.167
18. 2.671 2.568 2.484 2.413 2.353 2.302 2.257 2.217 2.182 2.151
19. 2.658 2.555 2.471 2.400 2.340 2.288 2.243 2.203 2.168 2.137
20. 2.646 2.544 2.459 2.388 2.328 2.276 2.230 2.191 2.155 2.124
21. 2.636 2.533 2.448 2.377 2.316 2.264 2.219 2.179 2.144 2.112
22. 2.626 2.523 2.438 2.367 2.306 2.254 2.208 2.168 2.133 2.102
23. 2.617 2.514 2.429 2.357 2.297 2.244 2.199 2.159 2.123 2.092
24. 2.609 2.505 2.420 2.349 2.288 2.235 2.190 2.150 2.114 2.082
25. 2.601 2.498 2.412 2.341 2.280 2.227 2.181 2.141 2.106 2.074
26. 2.594 2.491 2.405 2.333 2.272 2.220 2.174 2.134 2.098 2.066
27. 2.588 2.484 2.398 2.326 2.265 2.212 2.167 2.126 2.090 2.059
28. 2.582 2.478 2.392 2.320 2.259 2.206 2.160 2.119 2.084 2.052
29. 2.576 2.472 2.386 2.314 2.253 2.200 2.154 2.113 2.077 2.045
30. 2.570 2.466 2.380 2.308 2.247 2.194 2.148 2.107 2.071 2.039
31. 2.565 2.461 2.375 2.303 2.241 2.188 2.142 2.102 2.066 2.033
32. 2.561 2.456 2.370 2.298 2.236 2.183 2.137 2.096 2.060 2.028
33. 2.556 2.452 2.366 2.293 2.232 2.178 2.132 2.091 2.055 2.023
34. 2.552 2.447 2.361 2.289 2.227 2.174 2.127 2.087 2.050 2.018
35. 2.548 2.443 2.357 2.284 2.223 2.169 2.123 2.082 2.046 2.013
36. 2.544 2.439 2.353 2.280 2.219 2.165 2.119 2.078 2.042 2.009
37. 2.541 2.436 2.349 2.277 2.215 2.161 2.115 2.074 2.037 2.005
38. 2.537 2.432 2.346 2.273 2.211 2.158 2.111 2.070 2.034 2.001
39. 2.534 2.429 2.342 2.270 2.208 2.154 2.107 2.066 2.030 1.997
40. 2.531 2.426 2.339 2.266 2.204 2.151 2.104 2.063 2.026 1.994
41. 2.528 2.423 2.336 2.263 2.201 2.147 2.101 2.060 2.023 1.990
42. 2.525 2.420 2.333 2.260 2.198 2.144 2.098 2.056 2.020 1.987
43. 2.522 2.417 2.330 2.257 2.195 2.141 2.095 2.053 2.017 1.984
44. 2.520 2.415 2.328 2.255 2.192 2.139 2.092 2.050 2.014 1.981
45. 2.517 2.412 2.325 2.252 2.190 2.136 2.089 2.048 2.011 1.978
46. 2.515 2.410 2.323 2.250 2.187 2.133 2.086 2.045 2.008 1.976
47. 2.513 2.407 2.320 2.247 2.185 2.131 2.084 2.042 2.006 1.973
48. 2.511 2.405 2.318 2.245 2.182 2.128 2.081 2.040 2.003 1.970
49. 2.509 2.403 2.316 2.243 2.180 2.126 2.079 2.038 2.001 1.968
50. 2.507 2.401 2.314 2.241 2.178 2.124 2.077 2.035 1.999 1.966
51. 2.505 2.399 2.312 2.238 2.176 2.122 2.075 2.033 1.996 1.963
52. 2.503 2.397 2.310 2.236 2.174 2.120 2.073 2.031 1.994 1.961
53. 2.501 2.395 2.308 2.235 2.172 2.118 2.071 2.029 1.992 1.959
54. 2.499 2.394 2.306 2.233 2.170 2.116 2.069 2.027 1.990 1.957
55. 2.498 2.392 2.304 2.231 2.168 2.114 2.067 2.025 1.988 1.955
56. 2.496 2.390 2.303 2.229 2.167 2.112 2.065 2.023 1.986 1.953
57. 2.494 2.389 2.301 2.228 2.165 2.111 2.063 2.022 1.985 1.951
58. 2.493 2.387 2.300 2.226 2.163 2.109 2.062 2.020 1.983 1.950
59. 2.492 2.386 2.298 2.224 2.162 2.107 2.060 2.018 1.981 1.948
60. 2.490 2.384 2.297 2.223 2.160 2.106 2.058 2.017 1.980 1.946
61. 2.489 2.383 2.295 2.221 2.159 2.104 2.057 2.015 1.978 1.945
62. 2.487 2.381 2.294 2.220 2.157 2.103 2.055 2.014 1.976 1.943
63. 2.486 2.380 2.292 2.219 2.156 2.101 2.054 2.012 1.975 1.942
64. 2.485 2.379 2.291 2.217 2.154 2.100 2.053 2.011 1.974 1.940
65. 2.484 2.378 2.290 2.216 2.153 2.099 2.051 2.009 1.972 1.939
66. 2.483 2.376 2.289 2.215 2.152 2.097 2.050 2.008 1.971 1.937
67. 2.481 2.375 2.288 2.214 2.151 2.096 2.049 2.007 1.969 1.936
68. 2.480 2.374 2.286 2.212 2.149 2.095 2.047 2.005 1.968 1.935
69. 2.479 2.373 2.285 2.211 2.148 2.094 2.046 2.004 1.967 1.934
70. 2.478 2.372 2.284 2.210 2.147 2.093 2.045 2.003 1.966 1.932
71. 2.477 2.371 2.283 2.209 2.146 2.092 2.044 2.002 1.965 1.931
72. 2.476 2.370 2.282 2.208 2.145 2.090 2.043 2.001 1.963 1.930
73. 2.475 2.369 2.281 2.207 2.144 2.089 2.042 2.000 1.962 1.929
74. 2.474 2.368 2.280 2.206 2.143 2.088 2.041 1.999 1.961 1.928
75. 2.473 2.367 2.279 2.205 2.142 2.087 2.040 1.998 1.960 1.927
76. 2.473 2.366 2.278 2.204 2.141 2.086 2.039 1.997 1.959 1.926
77. 2.472 2.365 2.277 2.203 2.140 2.085 2.038 1.996 1.958 1.925
78. 2.471 2.364 2.276 2.202 2.139 2.084 2.037 1.995 1.957 1.924
79. 2.470 2.364 2.276 2.201 2.138 2.084 2.036 1.994 1.956 1.923
80. 2.469 2.363 2.275 2.201 2.137 2.083 2.035 1.993 1.955 1.922
81. 2.468 2.362 2.274 2.200 2.136 2.082 2.034 1.992 1.954 1.921
82. 2.468 2.361 2.273 2.199 2.136 2.081 2.033 1.991 1.953 1.920
83. 2.467 2.360 2.272 2.198 2.135 2.080 2.032 1.990 1.953 1.919
84. 2.466 2.360 2.272 2.197 2.134 2.079 2.031 1.989 1.952 1.918
85. 2.466 2.359 2.271 2.197 2.133 2.078 2.031 1.988 1.951 1.917
86. 2.465 2.358 2.270 2.196 2.133 2.078 2.030 1.988 1.950 1.916
87. 2.464 2.358 2.269 2.195 2.132 2.077 2.029 1.987 1.949 1.916
88. 2.463 2.357 2.269 2.194 2.131 2.076 2.028 1.986 1.948 1.915
89. 2.463 2.356 2.268 2.194 2.130 2.075 2.028 1.985 1.948 1.914
90. 2.462 2.356 2.267 2.193 2.130 2.075 2.027 1.985 1.947 1.913
91. 2.462 2.355 2.267 2.192 2.129 2.074 2.026 1.984 1.946 1.913
92. 2.461 2.354 2.266 2.192 2.128 2.073 2.025 1.983 1.946 1.912
93. 2.460 2.354 2.265 2.191 2.128 2.073 2.025 1.982 1.945 1.911
94. 2.460 2.353 2.265 2.190 2.127 2.072 2.024 1.982 1.944 1.910
95. 2.459 2.353 2.264 2.190 2.126 2.071 2.023 1.981 1.943 1.910
96. 2.459 2.352 2.264 2.189 2.126 2.071 2.023 1.980 1.943 1.909
97. 2.458 2.351 2.263 2.189 2.125 2.070 2.022 1.980 1.942 1.908
98. 2.458 2.351 2.262 2.188 2.125 2.070 2.022 1.979 1.942 1.908
99. 2.457 2.350 2.262 2.188 2.124 2.069 2.021 1.979 1.941 1.907
100. 2.457 2.350 2.261 2.187 2.123 2.068 2.020 1.978 1.940 1.907
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