Percentage Points of Student's t Distribution
The following is a table of critical t values for degrees of freedom from 1 to 120. Common 1- and 2-tailed alpha levels are included.
Click on the range that contains your degrees of freedom to jump to the desired table of critical t values.
1 - 10 | 11 - 20 | 21 - 30 | 31 - 40 | 41 - 50 | 51 - 60 |
61 - 70 | 71 - 80 | 81 - 90 | 91 - 100 | 101 - 110 | 111 - 120 |
of Freedom |
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1 | 1.000 | 1.376 | 1.963 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 | 636.619 |
2 | 0.816 | 1.061 | 1.386 | 1.886 | 2.920 | 4.303 | 6.964 | 9.925 | 31.599 |
3 | 0.765 | 0.978 | 1.250 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 12.924 |
4 | 0.741 | 0.941 | 1.189 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 8.610 |
5 | 0.727 | 0.920 | 1.156 | 1.476 | 2.015 | 2.570 | 3.365 | 4.032 | 6.869 |
6 | 0.718 | 0.906 | 1.134 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 5.959 |
7 | 0.711 | 0.896 | 1.119 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 5.408 |
8 | 0.706 | 0.889 | 1.108 | 1.397 | 1.859 | 2.306 | 2.896 | 3.355 | 5.041 |
9 | 0.703 | 0.883 | 1.100 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 4.781 |
10 | 0.700 | 0.879 | 1.093 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 4.587 |
of Freedom |
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11 | 0.697 | 0.876 | 1.088 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 4.437 |
12 | 0.695 | 0.873 | 1.083 | 1.356 | 1.782 | 2.179 | 2.681 | 3.054 | 4.318 |
13 | 0.694 | 0.870 | 1.079 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 4.221 |
14 | 0.692 | 0.868 | 1.076 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 4.140 |
15 | 0.691 | 0.866 | 1.073 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 4.073 |
16 | 0.690 | 0.865 | 1.071 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 4.015 |
17 | 0.689 | 0.863 | 1.069 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.965 |
18 | 0.688 | 0.862 | 1.067 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.922 |
19 | 0.688 | 0.861 | 1.065 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.883 |
20 | 0.687 | 0.860 | 1.064 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.849 |
of Freedom |
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21 | 0.686 | 0.859 | 1.063 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 3.819 |
22 | 0.686 | 0.858 | 1.061 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.792 |
23 | 0.685 | 0.858 | 1.060 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.768 |
24 | 0.685 | 0.857 | 1.059 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.745 |
25 | 0.684 | 0.856 | 1.058 | 1.316 | 1.708 | 2.059 | 2.485 | 2.787 | 3.725 |
26 | 0.684 | 0.856 | 1.057 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.707 |
27 | 0.684 | 0.855 | 1.057 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.689 |
28 | 0.683 | 0.855 | 1.056 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.674 |
29 | 0.683 | 0.854 | 1.055 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.659 |
30 | 0.683 | 0.854 | 1.055 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.646 |
of Freedom |
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31 | 0.682 | 0.853 | 1.054 | 1.309 | 1.696 | 2.040 | 2.453 | 2.744 | 3.633 |
32 | 0.682 | 0.853 | 1.053 | 1.308 | 1.694 | 2.037 | 2.449 | 2.738 | 3.622 |
33 | 0.682 | 0.853 | 1.053 | 1.308 | 1.692 | 2.035 | 2.445 | 2.733 | 3.611 |
34 | 0.682 | 0.852 | 1.052 | 1.307 | 1.691 | 2.032 | 2.441 | 2.728 | 3.601 |
35 | 0.681 | 0.852 | 1.052 | 1.306 | 1.689 | 2.030 | 2.438 | 2.724 | 3.591 |
36 | 0.681 | 0.852 | 1.052 | 1.305 | 1.688 | 2.028 | 2.434 | 2.719 | 3.582 |
37 | 0.681 | 0.851 | 1.051 | 1.305 | 1.687 | 2.026 | 2.431 | 2.715 | 3.574 |
38 | 0.681 | 0.851 | 1.051 | 1.304 | 1.686 | 2.024 | 2.428 | 2.711 | 3.566 |
39 | 0.681 | 0.851 | 1.050 | 1.304 | 1.685 | 2.023 | 2.426 | 2.708 | 3.558 |
40 | 0.681 | 0.851 | 1.050 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 | 3.551 |
of Freedom |
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41 | 0.680 | 0.850 | 1.050 | 1.303 | 1.683 | 2.020 | 2.421 | 2.701 | 3.544 |
42 | 0.680 | 0.850 | 1.049 | 1.302 | 1.682 | 2.018 | 2.418 | 2.698 | 3.538 |
43 | 0.680 | 0.850 | 1.049 | 1.302 | 1.681 | 2.017 | 2.416 | 2.695 | 3.532 |
44 | 0.680 | 0.850 | 1.049 | 1.301 | 1.680 | 2.015 | 2.414 | 2.692 | 3.526 |
45 | 0.680 | 0.850 | 1.048 | 1.301 | 1.679 | 2.014 | 2.412 | 2.689 | 3.520 |
46 | 0.680 | 0.850 | 1.048 | 1.300 | 1.679 | 2.013 | 2.410 | 2.687 | 3.515 |
47 | 0.680 | 0.849 | 1.048 | 1.300 | 1.678 | 2.012 | 2.408 | 2.684 | 3.510 |
48 | 0.680 | 0.849 | 1.048 | 1.299 | 1.677 | 2.011 | 2.406 | 2.682 | 3.505 |
49 | 0.679 | 0.849 | 1.047 | 1.299 | 1.677 | 2.010 | 2.405 | 2.680 | 3.500 |
50 | 0.679 | 0.849 | 1.047 | 1.299 | 1.676 | 2.009 | 2.403 | 2.678 | 3.496 |
of Freedom |
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51 | 0.679 | 0.849 | 1.047 | 1.298 | 1.675 | 2.008 | 2.402 | 2.676 | 3.492 |
52 | 0.679 | 0.849 | 1.047 | 1.298 | 1.675 | 2.007 | 2.400 | 2.674 | 3.488 |
53 | 0.679 | 0.848 | 1.047 | 1.298 | 1.674 | 2.006 | 2.399 | 2.672 | 3.484 |
54 | 0.679 | 0.848 | 1.046 | 1.297 | 1.674 | 2.005 | 2.397 | 2.670 | 3.480 |
55 | 0.679 | 0.848 | 1.046 | 1.297 | 1.673 | 2.004 | 2.396 | 2.668 | 3.476 |
56 | 0.679 | 0.848 | 1.046 | 1.297 | 1.673 | 2.003 | 2.395 | 2.666 | 3.473 |
57 | 0.679 | 0.848 | 1.046 | 1.296 | 1.672 | 2.002 | 2.393 | 2.665 | 3.469 |
58 | 0.679 | 0.848 | 1.046 | 1.296 | 1.672 | 2.002 | 2.392 | 2.663 | 3.466 |
59 | 0.679 | 0.848 | 1.046 | 1.296 | 1.671 | 2.001 | 2.391 | 2.662 | 3.463 |
60 | 0.679 | 0.848 | 1.045 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 | 3.460 |
of Freedom |
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61 | 0.678 | 0.848 | 1.045 | 1.295 | 1.670 | 2.000 | 2.389 | 2.659 | 3.457 |
62 | 0.678 | 0.847 | 1.045 | 1.295 | 1.670 | 1.999 | 2.388 | 2.657 | 3.454 |
63 | 0.678 | 0.847 | 1.045 | 1.295 | 1.669 | 1.998 | 2.387 | 2.656 | 3.452 |
64 | 0.678 | 0.847 | 1.045 | 1.295 | 1.669 | 1.998 | 2.386 | 2.655 | 3.449 |
65 | 0.678 | 0.847 | 1.045 | 1.295 | 1.669 | 1.997 | 2.385 | 2.654 | 3.446 |
66 | 0.678 | 0.847 | 1.045 | 1.294 | 1.668 | 1.997 | 2.384 | 2.652 | 3.444 |
67 | 0.678 | 0.847 | 1.044 | 1.294 | 1.668 | 1.996 | 2.383 | 2.651 | 3.442 |
68 | 0.678 | 0.847 | 1.044 | 1.294 | 1.667 | 1.995 | 2.382 | 2.650 | 3.439 |
69 | 0.678 | 0.847 | 1.044 | 1.294 | 1.667 | 1.995 | 2.382 | 2.649 | 3.437 |
70 | 0.678 | 0.847 | 1.044 | 1.294 | 1.667 | 1.994 | 2.381 | 2.648 | 3.435 |
of Freedom |
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71 | 0.678 | 0.847 | 1.044 | 1.294 | 1.667 | 1.994 | 2.380 | 2.647 | 3.433 |
72 | 0.678 | 0.847 | 1.044 | 1.293 | 1.666 | 1.993 | 2.379 | 2.646 | 3.431 |
73 | 0.678 | 0.847 | 1.044 | 1.293 | 1.666 | 1.993 | 2.378 | 2.645 | 3.429 |
74 | 0.678 | 0.847 | 1.044 | 1.293 | 1.666 | 1.993 | 2.378 | 2.644 | 3.427 |
75 | 0.678 | 0.846 | 1.044 | 1.293 | 1.665 | 1.992 | 2.377 | 2.643 | 3.425 |
76 | 0.678 | 0.846 | 1.043 | 1.293 | 1.665 | 1.992 | 2.376 | 2.642 | 3.423 |
77 | 0.678 | 0.846 | 1.043 | 1.293 | 1.665 | 1.991 | 2.376 | 2.641 | 3.421 |
78 | 0.678 | 0.846 | 1.043 | 1.292 | 1.665 | 1.991 | 2.375 | 2.640 | 3.420 |
79 | 0.678 | 0.846 | 1.043 | 1.292 | 1.664 | 1.990 | 2.374 | 2.639 | 3.418 |
80 | 0.677 | 0.846 | 1.043 | 1.292 | 1.664 | 1.990 | 2.374 | 2.639 | 3.416 |
of Freedom |
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81 | 0.677 | 0.846 | 1.043 | 1.292 | 1.664 | 1.990 | 2.373 | 2.638 | 3.415 |
82 | 0.677 | 0.846 | 1.043 | 1.292 | 1.664 | 1.989 | 2.373 | 2.637 | 3.413 |
83 | 0.677 | 0.846 | 1.043 | 1.292 | 1.663 | 1.989 | 2.372 | 2.636 | 3.412 |
84 | 0.677 | 0.846 | 1.043 | 1.292 | 1.663 | 1.989 | 2.371 | 2.636 | 3.410 |
85 | 0.677 | 0.846 | 1.043 | 1.292 | 1.663 | 1.988 | 2.371 | 2.635 | 3.409 |
86 | 0.677 | 0.846 | 1.043 | 1.291 | 1.663 | 1.988 | 2.370 | 2.634 | 3.407 |
87 | 0.677 | 0.846 | 1.043 | 1.291 | 1.663 | 1.988 | 2.370 | 2.633 | 3.406 |
88 | 0.677 | 0.846 | 1.042 | 1.291 | 1.662 | 1.987 | 2.369 | 2.633 | 3.404 |
89 | 0.677 | 0.846 | 1.042 | 1.291 | 1.662 | 1.987 | 2.369 | 2.632 | 3.403 |
90 | 0.677 | 0.846 | 1.042 | 1.291 | 1.662 | 1.987 | 2.368 | 2.631 | 3.402 |
of Freedom |
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91 | 0.677 | 0.846 | 1.042 | 1.291 | 1.662 | 1.986 | 2.368 | 2.631 | 3.401 |
92 | 0.677 | 0.846 | 1.042 | 1.291 | 1.662 | 1.986 | 2.367 | 2.630 | 3.399 |
93 | 0.677 | 0.846 | 1.042 | 1.291 | 1.661 | 1.986 | 2.367 | 2.630 | 3.398 |
94 | 0.677 | 0.845 | 1.042 | 1.291 | 1.661 | 1.986 | 2.367 | 2.629 | 3.397 |
95 | 0.677 | 0.845 | 1.042 | 1.291 | 1.661 | 1.985 | 2.366 | 2.628 | 3.396 |
96 | 0.677 | 0.845 | 1.042 | 1.290 | 1.661 | 1.985 | 2.366 | 2.628 | 3.395 |
97 | 0.677 | 0.845 | 1.042 | 1.290 | 1.661 | 1.985 | 2.365 | 2.627 | 3.394 |
98 | 0.677 | 0.845 | 1.042 | 1.290 | 1.661 | 1.984 | 2.365 | 2.627 | 3.392 |
99 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.984 | 2.365 | 2.626 | 3.391 |
100 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.984 | 2.364 | 2.626 | 3.390 |
of Freedom |
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101 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.984 | 2.364 | 2.625 | 3.389 |
102 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.983 | 2.363 | 2.625 | 3.388 |
103 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.983 | 2.363 | 2.624 | 3.387 |
104 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.983 | 2.363 | 2.624 | 3.386 |
105 | 0.677 | 0.845 | 1.042 | 1.290 | 1.659 | 1.983 | 2.362 | 2.623 | 3.386 |
106 | 0.677 | 0.845 | 1.042 | 1.289 | 1.659 | 1.983 | 2.362 | 2.623 | 3.385 |
107 | 0.677 | 0.845 | 1.041 | 1.289 | 1.659 | 1.982 | 2.362 | 2.622 | 3.384 |
108 | 0.677 | 0.845 | 1.041 | 1.289 | 1.659 | 1.982 | 2.361 | 2.622 | 3.383 |
109 | 0.677 | 0.845 | 1.041 | 1.289 | 1.659 | 1.982 | 2.361 | 2.622 | 3.382 |
110 | 0.677 | 0.845 | 1.041 | 1.289 | 1.659 | 1.982 | 2.361 | 2.621 | 3.381 |
of Freedom |
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111 | 0.677 | 0.845 | 1.041 | 1.289 | 1.659 | 1.982 | 2.360 | 2.621 | 3.380 |
112 | 0.677 | 0.845 | 1.041 | 1.289 | 1.658 | 1.981 | 2.360 | 2.620 | 3.379 |
113 | 0.677 | 0.845 | 1.041 | 1.289 | 1.658 | 1.981 | 2.360 | 2.620 | 3.379 |
114 | 0.677 | 0.845 | 1.041 | 1.289 | 1.658 | 1.981 | 2.359 | 2.620 | 3.378 |
115 | 0.677 | 0.845 | 1.041 | 1.289 | 1.658 | 1.981 | 2.359 | 2.619 | 3.377 |
116 | 0.677 | 0.845 | 1.041 | 1.289 | 1.658 | 1.981 | 2.359 | 2.619 | 3.376 |
117 | 0.676 | 0.845 | 1.041 | 1.289 | 1.658 | 1.980 | 2.359 | 2.618 | 3.376 |
118 | 0.676 | 0.845 | 1.041 | 1.289 | 1.658 | 1.980 | 2.358 | 2.618 | 3.375 |
119 | 0.676 | 0.845 | 1.041 | 1.289 | 1.658 | 1.980 | 2.358 | 2.618 | 3.374 |
120 | 0.676 | 0.845 | 1.041 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 3.373 |
The algorithm used to calculate these critical values
was created by B. E. Cooper. It is algorithm AS 3 in:
Griffiths, P., & Hill, I. D. (1986). Applied statistics
algorithms. Chichester, England: Ellis Horwood Limited.