Engineering Tables/Student's T-Distribution

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Table of Critical Values, tα,ν, in a Student T-Distribution with ν degrees of freedom and a confidence limit p where α=1–p. Student T-Distribution Table Diagram.svg
ν Confidence Limits (top) and α (bottom) for a One-Tailed Test.
60% 75% 80% 85% 90% 95% 97.5% 98% 99% 99.5% 99.75% 99.9% 99.95%
0.4 0.25 0.2 0.15 0.1 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005
1 0.32492 1.00000 1.37638 1.96261 3.07768 6.31375 12.70620 15.89454 31.82052 63.65674 127.32134 318.30884 636.61925
2 0.28868 0.81650 1.06066 1.38621 1.88562 2.91999 4.30265 4.84873 6.96456 9.92484 14.08905 22.32712 31.59905
3 0.27667 0.76489 0.97847 1.24978 1.63774 2.35336 3.18245 3.48191 4.54070 5.84091 7.45332 10.21453 12.92398
4 0.27072 0.74070 0.94096 1.18957 1.53321 2.13185 2.77645 2.99853 3.74695 4.60409 5.59757 7.17318 8.61030
5 0.26718 0.72669 0.91954 1.15577 1.47588 2.01505 2.57058 2.75651 3.36493 4.03214 4.77334 5.89343 6.86883
6 0.26483 0.71756 0.90570 1.13416 1.43976 1.94318 2.44691 2.61224 3.14267 3.70743 4.31683 5.20763 5.95882
7 0.26317 0.71114 0.89603 1.11916 1.41492 1.89458 2.36462 2.51675 2.99795 3.49948 4.02934 4.78529 5.40788
8 0.26192 0.70639 0.88889 1.10815 1.39682 1.85955 2.30600 2.44898 2.89646 3.35539 3.83252 4.50079 5.04131
9 0.26096 0.70272 0.88340 1.09972 1.38303 1.83311 2.26216 2.39844 2.82144 3.24984 3.68966 4.29681 4.78091
10 0.26018 0.69981 0.87906 1.09306 1.37218 1.81246 2.22814 2.35931 2.76377 3.16927 3.58141 4.14370 4.58689
11 0.25956 0.69745 0.87553 1.08767 1.36343 1.79588 2.20099 2.32814 2.71808 3.10581 3.49661 4.02470 4.43698
12 0.25903 0.69548 0.87261 1.08321 1.35622 1.78229 2.17881 2.30272 2.68100 3.05454 3.42844 3.92963 4.31779
13 0.25859 0.69383 0.87015 1.07947 1.35017 1.77093 2.16037 2.28160 2.65031 3.01228 3.37247 3.85198 4.22083
14 0.25821 0.69242 0.86805 1.07628 1.34503 1.76131 2.14479 2.26378 2.62449 2.97684 3.32570 3.78739 4.14045
15 0.25789 0.69120 0.86624 1.07353 1.34061 1.75305 2.13145 2.24854 2.60248 2.94671 3.28604 3.73283 4.07277
16 0.25760 0.69013 0.86467 1.07114 1.33676 1.74588 2.11991 2.23536 2.58349 2.92078 3.25199 3.68615 4.01500
17 0.25735 0.68920 0.86328 1.06903 1.33338 1.73961 2.10982 2.22385 2.56693 2.89823 3.22245 3.64577 3.96513
18 0.25712 0.68836 0.86205 1.06717 1.33039 1.73406 2.10092 2.21370 2.55238 2.87844 3.19657 3.61048 3.92165
19 0.25692 0.68762 0.86095 1.06551 1.32773 1.72913 2.09302 2.20470 2.53948 2.86093 3.17372 3.57940 3.88341
20 0.25674 0.68695 0.85996 1.06402 1.32534 1.72472 2.08596 2.19666 2.52798 2.84534 3.15340 3.55181 3.84952
21 0.25658 0.68635 0.85907 1.06267 1.32319 1.72074 2.07961 2.18943 2.51765 2.83136 3.13521 3.52715 3.81928
22 0.25643 0.68581 0.85827 1.06145 1.32124 1.71714 2.07387 2.18289 2.50832 2.81876 3.11882 3.50499 3.79213
23 0.25630 0.68531 0.85753 1.06034 1.31946 1.71387 2.06866 2.17696 2.49987 2.80734 3.10400 3.48496 3.76763
24 0.25617 0.68485 0.85686 1.05932 1.31784 1.71088 2.06390 2.17154 2.49216 2.79694 3.09051 3.46678 3.74540
25 0.25606 0.68443 0.85624 1.05838 1.31635 1.70814 2.05954 2.16659 2.48511 2.78744 3.07820 3.45019 3.72514
26 0.25595 0.68404 0.85567 1.05752 1.31497 1.70562 2.05553 2.16203 2.47863 2.77871 3.06691 3.43500 3.70661
27 0.25586 0.68368 0.85514 1.05673 1.31370 1.70329 2.05183 2.15782 2.47266 2.77068 3.05652 3.42103 3.68959
28 0.25577 0.68335 0.85465 1.05599 1.31253 1.70113 2.04841 2.15393 2.46714 2.76326 3.04693 3.40816 3.67391
29 0.25568 0.68304 0.85419 1.05530 1.31143 1.69913 2.04523 2.15033 2.46202 2.75639 3.03805 3.39624 3.65941
30 0.25561 0.68276 0.85377 1.05466 1.31042 1.69726 2.04227 2.14697 2.45726 2.75000 3.02980 3.38518 3.64596
40 0.25504 0.68067 0.85070 1.05005 1.30308 1.68385 2.02108 2.12291 2.42326 2.70446 2.97117 3.30688 3.55097
50 0.25470 0.67943 0.84887 1.04729 1.29871 1.67591 2.00856 2.10872 2.40327 2.67779 2.93696 3.26141 3.49601
60 0.25447 0.67860 0.84765 1.04547 1.29582 1.67065 2.00030 2.09936 2.39012 2.66028 2.91455 3.23171 3.46020
70 0.25431 0.67801 0.84679 1.04417 1.29376 1.66691 1.99444 2.09273 2.38081 2.64790 2.89873 3.21079 3.43501
80 0.25419 0.67757 0.84614 1.04320 1.29222 1.66412 1.99006 2.08778 2.37387 2.63869 2.88697 3.19526 3.41634
90 0.25410 0.67723 0.84563 1.04244 1.29103 1.66196 1.98667 2.08394 2.36850 2.63157 2.87788 3.18327 3.40194
100 0.25402 0.67695 0.84523 1.04184 1.29007 1.66023 1.98397 2.08088 2.36422 2.62589 2.87065 3.17374 3.39049
500 0.25348 0.67498 0.84234 1.03751 1.28325 1.64791 1.96472 2.05912 2.33383 2.58570 2.81955 3.10661 3.31009
1000 0.25341 0.67474 0.84198 1.03697 1.28240 1.64638 1.96234 2.05643 2.33008 2.58075 2.81328 3.09840 3.30028
0.25335 0.67449 0.84162 1.03643 1.28155 1.64485 1.95996 2.05375 2.32635 2.57583 2.80703 3.09023 3.29053
Explanatory Notes
  • For a Two-Tailed Test, use the α here that corresponds to half the two-tailed α.
    • For example if a two-tailed confidence limit of 90% is desired (α=0.1), use a one-tailed α from this table of 0.05
  • In the limit ν=∞, this distribution is equivalent to a normal distribution X~N(0,1)