Table of the Standard $t$ distribution



Let $X \sim t_k=t(k)$, $k$ = # degrees of freedom \[ f(x;k) = \frac{\Gamma(\frac{k+1}{2})}{\sqrt{k\pi}\Gamma(\frac{k}{2})}\left( 1+\frac{x^2}{k} \right)^{-\frac{k+1}{2}} \] $P(X \leq x)$ is given by: \[ \int_{-\infty}^x f(x;k)dx \]



$t_{0.999}$ $t_{0.9975}$ $t_{0.995}$ $t_{0.99}$ $t_{0.98}$ $t_{0.975}$ $t_{0.95}$ $t_{0.9}$ $t_{0.85}$ $t_{0.8}$ $t_{0.75}$
1 318.309 127.321 63.657 31.821 15.895 12.706 6.314 3.078 1.963 1.376 1.000
2 22.327 14.089 9.925 6.965 4.849 4.303 2.920 1.886 1.386 1.061 0.816
3 10.215 7.453 5.841 4.541 3.482 3.182 2.353 1.638 1.250 0.978 0.765
4 7.173 5.598 4.604 3.747 2.999 2.776 2.132 1.533 1.190 0.941 0.741
5 5.893 4.773 4.032 3.365 2.757 2.571 2.015 1.476 1.156 0.920 0.727
6 5.208 4.317 3.707 3.143 2.612 2.447 1.943 1.440 1.134 0.906 0.718
7 4.785 4.029 3.499 2.998 2.517 2.365 1.895 1.415 1.119 0.896 0.711
8 4.501 3.833 3.355 2.896 2.449 2.306 1.860 1.397 1.108 0.889 0.706
9 4.297 3.690 3.250 2.821 2.398 2.262 1.833 1.383 1.100 0.883 0.703
10 4.144 3.581 3.169 2.764 2.359 2.228 1.812 1.372 1.093 0.879 0.700
11 4.025 3.497 3.106 2.718 2.328 2.201 1.796 1.363 1.088 0.876 0.697
12 3.930 3.428 3.055 2.681 2.303 2.179 1.782 1.356 1.083 0.873 0.695
13 3.852 3.372 3.012 2.650 2.282 2.160 1.771 1.350 1.079 0.870 0.694
14 3.787 3.326 2.977 2.624 2.264 2.145 1.761 1.345 1.076 0.868 0.692
15 3.733 3.286 2.947 2.602 2.249 2.131 1.753 1.341 1.074 0.866 0.691
16 3.686 3.252 2.921 2.583 2.235 2.120 1.746 1.337 1.071 0.865 0.690
17 3.646 3.222 2.898 2.567 2.224 2.110 1.740 1.333 1.069 0.863 0.689
18 3.610 3.197 2.878 2.552 2.214 2.101 1.734 1.330 1.067 0.862 0.688
19 3.579 3.174 2.861 2.539 2.205 2.093 1.729 1.328 1.066 0.861 0.688
20 3.552 3.153 2.845 2.528 2.197 2.086 1.725 1.325 1.064 0.860 0.687
21 3.527 3.135 2.831 2.518 2.189 2.080 1.721 1.323 1.063 0.859 0.686
22 3.505 3.119 2.819 2.508 2.183 2.074 1.717 1.321 1.061 0.858 0.686
23 3.485 3.104 2.807 2.500 2.177 2.069 1.714 1.319 1.060 0.858 0.685
24 3.467 3.091 2.797 2.492 2.172 2.064 1.711 1.318 1.059 0.857 0.685
25 3.450 3.078 2.787 2.485 2.167 2.060 1.708 1.316 1.058 0.856 0.684
26 3.435 3.067 2.779 2.479 2.162 2.056 1.706 1.315 1.058 0.856 0.684
27 3.421 3.057 2.771 2.473 2.158 2.052 1.703 1.314 1.057 0.855 0.684
28 3.408 3.047 2.763 2.467 2.154 2.048 1.701 1.313 1.056 0.855 0.683
29 3.396 3.038 2.756 2.462 2.150 2.045 1.699 1.311 1.055 0.854 0.683
30 3.385 3.030 2.750 2.457 2.147 2.042 1.697 1.310 1.055 0.854 0.683
40 3.307 2.971 2.704 2.423 2.123 2.021 1.684 1.303 1.050 0.851 0.681
50 3.261 2.937 2.678 2.403 2.109 2.009 1.676 1.299 1.047 0.849 0.679
60 3.232 2.915 2.660 2.390 2.099 2.000 1.671 1.296 1.045 0.848 0.679
70 3.211 2.899 2.648 2.381 2.093 1.994 1.667 1.294 1.044 0.847 0.678