Critical values for the \(t\)-distribution
Values of the \(t\)-distribution, given the degrees of freedom (rows)
and tail probability \(p\) (columns). These can be used for critical
values for a given confidence level.
| 1 |
1.963 |
3.078 |
6.314 |
12.71 |
15.90 |
31.82 |
63.66 |
127.3 |
318.3 |
636.6 |
| 2 |
1.386 |
1.886 |
2.920 |
4.303 |
4.849 |
6.965 |
9.925 |
14.09 |
22.33 |
31.60 |
| 3 |
1.250 |
1.638 |
2.353 |
3.182 |
3.482 |
4.541 |
5.841 |
7.453 |
10.22 |
12.92 |
| 4 |
1.190 |
1.533 |
2.132 |
2.776 |
2.999 |
3.747 |
4.604 |
5.598 |
7.173 |
8.610 |
| 5 |
1.156 |
1.476 |
2.015 |
2.571 |
2.757 |
3.365 |
4.032 |
4.773 |
5.893 |
6.869 |
| 6 |
1.134 |
1.440 |
1.943 |
2.447 |
2.612 |
3.143 |
3.707 |
4.317 |
5.208 |
5.959 |
| 7 |
1.119 |
1.415 |
1.895 |
2.365 |
2.517 |
2.998 |
3.499 |
4.029 |
4.785 |
5.408 |
| 8 |
1.108 |
1.397 |
1.860 |
2.306 |
2.449 |
2.896 |
3.355 |
3.833 |
4.501 |
5.041 |
| 9 |
1.100 |
1.383 |
1.833 |
2.262 |
2.398 |
2.821 |
3.250 |
3.690 |
4.297 |
4.781 |
| 10 |
1.093 |
1.372 |
1.812 |
2.228 |
2.359 |
2.764 |
3.169 |
3.581 |
4.144 |
4.587 |
| 11 |
1.088 |
1.363 |
1.796 |
2.201 |
2.328 |
2.718 |
3.106 |
3.497 |
4.025 |
4.437 |
| 12 |
1.083 |
1.356 |
1.782 |
2.179 |
2.303 |
2.681 |
3.055 |
3.428 |
3.930 |
4.318 |
| 13 |
1.079 |
1.350 |
1.771 |
2.160 |
2.282 |
2.650 |
3.012 |
3.372 |
3.852 |
4.221 |
| 14 |
1.076 |
1.345 |
1.761 |
2.145 |
2.264 |
2.624 |
2.977 |
3.326 |
3.787 |
4.140 |
| 15 |
1.074 |
1.341 |
1.753 |
2.131 |
2.249 |
2.602 |
2.947 |
3.286 |
3.733 |
4.073 |
| 16 |
1.071 |
1.337 |
1.746 |
2.120 |
2.235 |
2.583 |
2.921 |
3.252 |
3.686 |
4.015 |
| 17 |
1.069 |
1.333 |
1.740 |
2.110 |
2.224 |
2.567 |
2.898 |
3.222 |
3.646 |
3.965 |
| 18 |
1.067 |
1.330 |
1.734 |
2.101 |
2.214 |
2.552 |
2.878 |
3.197 |
3.610 |
3.922 |
| 19 |
1.066 |
1.328 |
1.729 |
2.093 |
2.205 |
2.539 |
2.861 |
3.174 |
3.579 |
3.883 |
| 20 |
1.064 |
1.325 |
1.725 |
2.086 |
2.197 |
2.528 |
2.845 |
3.153 |
3.552 |
3.850 |
| 21 |
1.063 |
1.323 |
1.721 |
2.080 |
2.189 |
2.518 |
2.831 |
3.135 |
3.527 |
3.819 |
| 22 |
1.061 |
1.321 |
1.717 |
2.074 |
2.183 |
2.508 |
2.819 |
3.119 |
3.505 |
3.792 |
| 23 |
1.060 |
1.319 |
1.714 |
2.069 |
2.177 |
2.500 |
2.807 |
3.104 |
3.485 |
3.768 |
| 24 |
1.059 |
1.318 |
1.711 |
2.064 |
2.172 |
2.492 |
2.797 |
3.091 |
3.467 |
3.745 |
| 25 |
1.058 |
1.316 |
1.708 |
2.060 |
2.167 |
2.485 |
2.787 |
3.078 |
3.450 |
3.725 |
| 26 |
1.058 |
1.315 |
1.706 |
2.056 |
2.162 |
2.479 |
2.779 |
3.067 |
3.435 |
3.707 |
| 27 |
1.057 |
1.314 |
1.703 |
2.052 |
2.158 |
2.473 |
2.771 |
3.057 |
3.421 |
3.690 |
| 28 |
1.056 |
1.313 |
1.701 |
2.048 |
2.154 |
2.467 |
2.763 |
3.047 |
3.408 |
3.674 |
| 29 |
1.055 |
1.311 |
1.699 |
2.045 |
2.150 |
2.462 |
2.756 |
3.038 |
3.396 |
3.659 |
| 30 |
1.055 |
1.310 |
1.697 |
2.042 |
2.147 |
2.457 |
2.750 |
3.030 |
3.385 |
3.646 |
| 40 |
1.050 |
1.303 |
1.684 |
2.021 |
2.123 |
2.423 |
2.704 |
2.971 |
3.307 |
3.551 |
| 50 |
1.047 |
1.299 |
1.676 |
2.009 |
2.109 |
2.403 |
2.678 |
2.937 |
3.261 |
3.496 |
| 60 |
1.045 |
1.296 |
1.671 |
2.000 |
2.099 |
2.390 |
2.660 |
2.915 |
3.232 |
3.460 |
| 120 |
1.041 |
1.289 |
1.658 |
1.980 |
2.076 |
2.358 |
2.617 |
2.860 |
3.160 |
3.373 |
| 10000 |
1.036 |
1.282 |
1.645 |
1.960 |
2.054 |
2.327 |
2.576 |
2.808 |
3.091 |
3.291 |
|
70% |
80% |
90% |
95% |
96% |
98% |
99% |
99.5% |
99.8% |
99.9% |