Table 8: Student's t Quantiles (Percentiles)
The p-th quantiles (i.e., 100p-th percentiles) of the Student's t distribution are tabulated for degrees of freedom m = 1, 2, ...,100 and p = 0.90, 0.95, 0.975, 0.99, 0.995, 0.999 and 0.9995.
Example: The 0.95-th quantile of the Student's t distribution with 10 degrees of freedom is 1.81246.
| 100p | |||||||
| m | 90.0 | 95.0 | 97.5 | 99.0 | 99.5 | 99.9 | 99.95 |
| 1 | 3.07768 | 6.31375 | 12.70615 | 31.82096 | 63.65590 | 318.28880 | 636.57760 |
| 2 | 1.88562 | 2.91999 | 4.30266 | 6.96455 | 9.92499 | 22.32846 | 31.59977 |
| 3 | 1.63775 | 2.35336 | 3.18245 | 4.54071 | 5.84085 | 10.21428 | 12.92443 |
| 4 | 1.53321 | 2.13185 | 2.77645 | 3.74694 | 4.60408 | 7.17293 | 8.61008 |
| 5 | 1.47588 | 2.01505 | 2.57058 | 3.36493 | 4.03212 | 5.89353 | 6.86850 |
| 6 | 1.43976 | 1.94318 | 2.44691 | 3.14267 | 3.70743 | 5.20755 | 5.95872 |
| 7 | 1.41492 | 1.89458 | 2.36462 | 2.99795 | 3.49948 | 4.78525 | 5.40807 |
| 8 | 1.39682 | 1.85955 | 2.30601 | 2.89647 | 3.35538 | 4.50076 | 5.04137 |
| 9 | 1.38303 | 1.83311 | 2.26216 | 2.82143 | 3.24984 | 4.29689 | 4.78089 |
| 10 | 1.37218 | 1.81246 | 2.22814 | 2.76377 | 3.16926 | 4.14366 | 4.58676 |
| 11 | 1.36343 | 1.79588 | 2.20099 | 2.71808 | 3.10582 | 4.02477 | 4.43688 |
| 12 | 1.35622 | 1.78229 | 2.17881 | 2.68099 | 3.05454 | 3.92960 | 4.31784 |
| 13 | 1.35017 | 1.77093 | 2.16037 | 2.65030 | 3.01228 | 3.85204 | 4.22093 |
| 14 | 1.34503 | 1.76131 | 2.14479 | 2.62449 | 2.97685 | 3.78743 | 4.14031 |
| 15 | 1.34061 | 1.75305 | 2.13145 | 2.60248 | 2.94673 | 3.73286 | 4.07279 |
| 16 | 1.33676 | 1.74588 | 2.11990 | 2.58349 | 2.92079 | 3.68615 | 4.01487 |
| 17 | 1.33338 | 1.73961 | 2.10982 | 2.56694 | 2.89823 | 3.64576 | 3.96511 |
| 18 | 1.33039 | 1.73406 | 2.10092 | 2.55238 | 2.87844 | 3.61048 | 3.92174 |
| 19 | 1.32773 | 1.72913 | 2.09302 | 2.53948 | 2.86094 | 3.57933 | 3.88332 |
| 20 | 1.32534 | 1.72472 | 2.08596 | 2.52798 | 2.84534 | 3.55183 | 3.84956 |
| 21 | 1.32319 | 1.72074 | 2.07961 | 2.51765 | 2.83137 | 3.52709 | 3.81930 |
| 22 | 1.32124 | 1.71714 | 2.07388 | 2.50832 | 2.81876 | 3.50497 | 3.79223 |
| 23 | 1.31946 | 1.71387 | 2.06865 | 2.49987 | 2.80734 | 3.48497 | 3.76764 |
| 24 | 1.31784 | 1.71088 | 2.06390 | 2.49216 | 2.79695 | 3.46678 | 3.74537 |
| 25 | 1.31635 | 1.70814 | 2.05954 | 2.48510 | 2.78744 | 3.45019 | 3.72514 |
| 26 | 1.31497 | 1.70562 | 2.05553 | 2.47863 | 2.77872 | 3.43498 | 3.70666 |
| 27 | 1.31370 | 1.70329 | 2.05183 | 2.47266 | 2.77068 | 3.42101 | 3.68949 |
| 28 | 1.31253 | 1.70113 | 2.04841 | 2.46714 | 2.76326 | 3.40820 | 3.67392 |
| 29 | 1.31143 | 1.69913 | 2.04523 | 2.46202 | 2.75639 | 3.39627 | 3.65952 |
| 30 | 1.31042 | 1.69726 | 2.04227 | 2.45726 | 2.74998 | 3.38521 | 3.64598 |
| 31 | 1.30946 | 1.69552 | 2.03951 | 2.45283 | 2.74404 | 3.37488 | 3.63347 |
| 32 | 1.30857 | 1.69389 | 2.03693 | 2.44868 | 2.73849 | 3.36528 | 3.62183 |
| 33 | 1.30774 | 1.69236 | 2.03452 | 2.44479 | 2.73329 | 3.35633 | 3.61091 |
| 34 | 1.30695 | 1.69092 | 2.03224 | 2.44115 | 2.72839 | 3.34796 | 3.60073 |
| 35 | 1.30621 | 1.68957 | 2.03011 | 2.43772 | 2.72381 | 3.34003 | 3.59112 |
| 36 | 1.30551 | 1.68830 | 2.02809 | 2.43450 | 2.71948 | 3.33261 | 3.58210 |
| 37 | 1.30485 | 1.68709 | 2.02619 | 2.43144 | 2.71541 | 3.32562 | 3.57366 |
| 38 | 1.30423 | 1.68595 | 2.02439 | 2.42857 | 2.71157 | 3.31900 | 3.56566 |
| 39 | 1.30364 | 1.68488 | 2.02269 | 2.42584 | 2.70791 | 3.31274 | 3.55809 |
| 40 | 1.30308 | 1.68385 | 2.02107 | 2.42326 | 2.70446 | 3.30692 | 3.55096 |
| 41 | 1.30254 | 1.68288 | 2.01954 | 2.42080 | 2.70118 | 3.30127 | 3.54418 |
| 42 | 1.30204 | 1.68195 | 2.01808 | 2.41847 | 2.69807 | 3.29595 | 3.53775 |
| 43 | 1.30155 | 1.68107 | 2.01669 | 2.41625 | 2.69510 | 3.29089 | 3.53163 |
| 44 | 1.30109 | 1.68023 | 2.01537 | 2.41413 | 2.69228 | 3.28607 | 3.52580 |
| 45 | 1.30065 | 1.67943 | 2.01410 | 2.41212 | 2.68959 | 3.28148 | 3.52025 |
| 46 | 1.30023 | 1.67866 | 2.01290 | 2.41019 | 2.68701 | 3.27710 | 3.51496 |
| 47 | 1.29982 | 1.67793 | 2.01174 | 2.40835 | 2.68456 | 3.27291 | 3.50990 |
| 48 | 1.29944 | 1.67722 | 2.01063 | 2.40658 | 2.68220 | 3.26891 | 3.50507 |
| 49 | 1.29907 | 1.67655 | 2.00958 | 2.40489 | 2.67995 | 3.26508 | 3.50044 |
| 50 | 1.29871 | 1.67591 | 2.00856 | 2.40327 | 2.67779 | 3.26141 | 3.49601 |
| 51 | 1.29837 | 1.67528 | 2.00758 | 2.40172 | 2.67572 | 3.25789 | 3.49177 |
| 52 | 1.29805 | 1.67469 | 2.00665 | 2.40022 | 2.67373 | 3.25451 | 3.48769 |
| 53 | 1.29773 | 1.67412 | 2.00575 | 2.39879 | 2.67182 | 3.25127 | 3.48378 |
| 54 | 1.29743 | 1.67356 | 2.00488 | 2.39741 | 2.66998 | 3.24815 | 3.48002 |
| 55 | 1.29713 | 1.67303 | 2.00404 | 2.39608 | 2.66822 | 3.24515 | 3.47640 |
| 56 | 1.29685 | 1.67252 | 2.00324 | 2.39480 | 2.66651 | 3.24226 | 3.47292 |
| 57 | 1.29658 | 1.67203 | 2.00247 | 2.39357 | 2.66487 | 3.23948 | 3.46956 |
| 58 | 1.29632 | 1.67155 | 2.00172 | 2.39238 | 2.66329 | 3.23680 | 3.46633 |
| 59 | 1.29607 | 1.67109 | 2.00100 | 2.39123 | 2.66176 | 3.23421 | 3.46321 |
| 60 | 1.29582 | 1.67065 | 2.00030 | 2.39012 | 2.66028 | 3.23171 | 3.46020 |
| 61 | 1.29558 | 1.67022 | 1.99962 | 2.38905 | 2.65886 | 3.22930 | 3.45729 |
| 62 | 1.29536 | 1.66980 | 1.99897 | 2.38801 | 2.65748 | 3.22696 | 3.45448 |
| 63 | 1.29513 | 1.66940 | 1.99834 | 2.38701 | 2.65615 | 3.22471 | 3.45177 |
| 64 | 1.29492 | 1.66901 | 1.99773 | 2.38604 | 2.65485 | 3.22253 | 3.44914 |
| 65 | 1.29471 | 1.66864 | 1.99714 | 2.38510 | 2.65360 | 3.22041 | 3.44660 |
| 66 | 1.29451 | 1.66827 | 1.99656 | 2.38419 | 2.65239 | 3.21837 | 3.44414 |
| 67 | 1.29432 | 1.66792 | 1.99601 | 2.38330 | 2.65122 | 3.21639 | 3.44175 |
| 68 | 1.29413 | 1.66757 | 1.99547 | 2.38245 | 2.65008 | 3.21446 | 3.43944 |
| 69 | 1.29394 | 1.66724 | 1.99495 | 2.38161 | 2.64898 | 3.21260 | 3.43719 |
| 70 | 1.29376 | 1.66691 | 1.99444 | 2.38081 | 2.64790 | 3.21079 | 3.43501 |
| 71 | 1.29359 | 1.66660 | 1.99394 | 2.38002 | 2.64686 | 3.20903 | 3.43290 |
| 72 | 1.29342 | 1.66629 | 1.99346 | 2.37926 | 2.64585 | 3.20733 | 3.43085 |
| 73 | 1.29326 | 1.66600 | 1.99300 | 2.37852 | 2.64487 | 3.20567 | 3.42885 |
| 74 | 1.29310 | 1.66571 | 1.99254 | 2.37780 | 2.64391 | 3.20406 | 3.42692 |
| 75 | 1.29294 | 1.66543 | 1.99210 | 2.37710 | 2.64298 | 3.20249 | 3.42503 |
| 76 | 1.29279 | 1.66515 | 1.99167 | 2.37642 | 2.64208 | 3.20096 | 3.42320 |
| 77 | 1.29264 | 1.66488 | 1.99125 | 2.37576 | 2.64120 | 3.19948 | 3.42141 |
| 78 | 1.29250 | 1.66462 | 1.99085 | 2.37511 | 2.64034 | 3.19804 | 3.41968 |
| 79 | 1.29236 | 1.66437 | 1.99045 | 2.37448 | 2.63950 | 3.19663 | 3.41799 |
| 80 | 1.29222 | 1.66412 | 1.99006 | 2.37387 | 2.63869 | 3.19526 | 3.41634 |
| 81 | 1.29209 | 1.66388 | 1.98969 | 2.37327 | 2.63790 | 3.19392 | 3.41473 |
| 82 | 1.29196 | 1.66365 | 1.98932 | 2.37269 | 2.63712 | 3.19262 | 3.41317 |
| 83 | 1.29183 | 1.66342 | 1.98896 | 2.37212 | 2.63637 | 3.19135 | 3.41164 |
| 84 | 1.29171 | 1.66320 | 1.98861 | 2.37156 | 2.63563 | 3.19011 | 3.41015 |
| 85 | 1.29159 | 1.66298 | 1.98827 | 2.37102 | 2.63491 | 3.18890 | 3.40870 |
| 86 | 1.29147 | 1.66277 | 1.98793 | 2.37049 | 2.63421 | 3.18772 | 3.40728 |
| 87 | 1.29136 | 1.66256 | 1.98761 | 2.36998 | 2.63353 | 3.18657 | 3.40590 |
| 88 | 1.29125 | 1.66235 | 1.98729 | 2.36947 | 2.63286 | 3.18544 | 3.40455 |
| 89 | 1.29114 | 1.66216 | 1.98698 | 2.36898 | 2.63220 | 3.18434 | 3.40323 |
| 90 | 1.29103 | 1.66196 | 1.98667 | 2.36850 | 2.63157 | 3.18327 | 3.40194 |
| 91 | 1.29092 | 1.66177 | 1.98638 | 2.36803 | 2.63094 | 3.18222 | 3.40067 |
| 92 | 1.29082 | 1.66159 | 1.98609 | 2.36757 | 2.63033 | 3.18119 | 3.39944 |
| 93 | 1.29072 | 1.66140 | 1.98580 | 2.36712 | 2.62973 | 3.18019 | 3.39824 |
| 94 | 1.29062 | 1.66123 | 1.98552 | 2.36667 | 2.62915 | 3.17921 | 3.39706 |
| 95 | 1.29053 | 1.66105 | 1.98525 | 2.36624 | 2.62858 | 3.17825 | 3.39590 |
| 96 | 1.29043 | 1.66088 | 1.98498 | 2.36582 | 2.62802 | 3.17731 | 3.39477 |
| 97 | 1.29034 | 1.66071 | 1.98472 | 2.36541 | 2.62747 | 3.17639 | 3.39367 |
| 98 | 1.29025 | 1.66055 | 1.98447 | 2.36500 | 2.62693 | 3.17549 | 3.39259 |
| 99 | 1.29016 | 1.66039 | 1.98422 | 2.36461 | 2.62641 | 3.17460 | 3.39153 |
| 100 | 1.29007 | 1.66023 | 1.98397 | 2.36422 | 2.62589 | 3.17374 | 3.39049 |
Tabulated by S L C Saw
