# Engineering Tables/Student's T-Distribution

Table of Critical Values, t$_{α,ν}$, in a Student T-Distribution with ν degrees of freedom and a confidence limit p where α=1–p. :
| ν | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. | Confidence Limits (top) and α (bottom) for a One-Tailed Test. |
| ν | 60% | 75% | 80% | 85% | 90% | 95% | 97.5% | 98% | 99% | 99.5% | 99.75% | 99.9% | 99.95% |
| ν | 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) ||||||||||||||