t distribution table

Complete t distribution table with critical values for one-tailed and two-tailed tests. Interactive calculator included.

df 0.500 0.200 0.100 0.050 0.020 0.010 0.001
0.2500 0.1000 0.0500 0.0250 0.0100 0.0050 0.0005
1 1.000 3.078 6.314 12.706 31.821 63.657 636.619
2 0.816 1.886 2.920 4.303 6.965 9.925 31.599
3 0.765 1.638 2.353 3.182 4.541 5.841 12.924
4 0.741 1.533 2.132 2.776 3.747 4.604 8.610
5 0.727 1.476 2.015 2.571 3.365 4.032 6.869
6 0.718 1.440 1.943 2.447 3.143 3.707 5.959
7 0.711 1.415 1.895 2.365 2.998 3.499 5.408
8 0.706 1.397 1.860 2.306 2.896 3.355 5.041
9 0.703 1.383 1.833 2.262 2.821 3.250 4.781
10 0.700 1.372 1.812 2.228 2.764 3.169 4.587
11 0.697 1.363 1.796 2.201 2.718 3.106 4.437
12 0.695 1.356 1.782 2.179 2.681 3.055 4.318
13 0.694 1.350 1.771 2.160 2.650 3.012 4.221
14 0.692 1.345 1.761 2.145 2.624 2.977 4.140
15 0.691 1.341 1.753 2.131 2.602 2.947 4.073
16 0.690 1.337 1.746 2.120 2.583 2.921 4.015
17 0.689 1.333 1.740 2.110 2.567 2.898 3.965
18 0.688 1.330 1.734 2.101 2.552 2.878 3.922
19 0.688 1.328 1.729 2.093 2.539 2.861 3.883
20 0.687 1.325 1.725 2.086 2.528 2.845 3.850
21 0.686 1.323 1.721 2.080 2.518 2.831 3.819
22 0.686 1.321 1.717 2.074 2.508 2.819 3.792
23 0.685 1.319 1.714 2.069 2.500 2.807 3.768
24 0.685 1.318 1.711 2.064 2.492 2.797 3.745
25 0.684 1.316 1.708 2.060 2.485 2.787 3.725
26 0.684 1.315 1.706 2.056 2.479 2.779 3.707
27 0.684 1.314 1.703 2.052 2.473 2.771 3.690
28 0.683 1.313 1.701 2.048 2.467 2.763 3.674
29 0.683 1.311 1.699 2.045 2.462 2.756 3.659
30 0.683 1.310 1.697 2.042 2.457 2.750 3.646
35 0.682 1.306 1.690 2.030 2.438 2.724 3.591
40 0.681 1.303 1.684 2.021 2.423 2.704 3.551
45 0.680 1.301 1.679 2.014 2.412 2.690 3.520
50 0.679 1.299 1.676 2.009 2.403 2.678 3.496
60 0.679 1.296 1.671 2.000 2.390 2.660 3.460
70 0.678 1.294 1.667 1.994 2.381 2.648 3.435
80 0.678 1.292 1.664 1.990 2.374 2.639 3.416
90 0.677 1.291 1.662 1.987 2.368 2.632 3.402
100 0.677 1.290 1.660 1.984 2.364 2.626 3.390
120 0.677 1.289 1.658 1.980 2.358 2.617 3.373
150 0.676 1.287 1.655 1.976 2.351 2.609 3.357
200 0.676 1.286 1.653 1.972 2.345 2.601 3.340
500 0.675 1.283 1.648 1.965 2.334 2.586 3.310
1000 0.675 1.282 1.646 1.962 2.330 2.581 3.300
∞ 0.674 1.282 1.645 1.960 2.326 2.576 3.291

What is the t distribution?

Student’s t distribution is a probability distribution used when estimating population parameters with small samples or unknown population variance. It resembles the normal distribution but has heavier tails, which account for the extra uncertainty.

How to use this table

  1. Calculate your t-statistic: \(t = \dfrac{\bar{x} - \mu_0}{s / \sqrt{n}}\)
  2. Determine your degrees of freedom: \(df = n - 1\)
  3. Choose your significance level \(\alpha\) and whether the test is one-tailed or two-tailed
  4. Find the critical value at the intersection of the df row and \(\alpha\) column
  5. If \(|t| \geq t_{\text{critical}}\), reject \(H_0\)

Worked example

A researcher measures 16 patients (\(n = 16\), \(df = 15\)) and obtains \(t = 2.35\) for a two-tailed test at \(\alpha = 0.05\). The critical value is \(t_{0.05, 15} = 2.131\). Since \(2.35 > 2.131\), the result is statistically significant.