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T-Table (Critical Values of t Distribution)
This t-table lists the critical values of Student’s t distribution for the significance levels used in tests and confidence intervals. The column headers give the one-tailed α (area in one tail) and the equivalent two-tailed α; the rows are degrees of freedom from 1 to 30, then selected larger values up to 1000, and the final row is the normal-distribution limit.
To use it, find your degrees of freedom (n − 1 for a one-sample or paired t-test) and the column for your α and tail. For a 95% confidence interval with df = 12, read the two-tailed 0.05 column: 2.179. If your df is not listed, use the lookup box for the exact value rather than the next-smaller row, which is what a printed table would force you to do.
Values are rounded to three decimals and agree with R’s qt, SciPy’s t.ppf and Excel’s T.INV.2T. For p-values from a t statistic use the t distribution calculator, and for a complete test see the one-sample t-test.
Exact lookup
T-Table (Critical Values of t Distribution)
| df | one-tail 0.1 two-tail 0.2 | one-tail 0.05 two-tail 0.1 | one-tail 0.025 two-tail 0.05 | one-tail 0.01 two-tail 0.02 | one-tail 0.005 two-tail 0.01 | one-tail 0.001 two-tail 0.002 | one-tail 0.0005 two-tail 0.001 |
|---|---|---|---|---|---|---|---|
| 1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 | 318.309 | 636.619 |
| 2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | 22.327 | 31.599 |
| 3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 10.215 | 12.924 |
| 4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 7.173 | 8.610 |
| 5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 5.893 | 6.869 |
| 6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 5.208 | 5.959 |
| 7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 4.785 | 5.408 |
| 8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 | 4.501 | 5.041 |
| 9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 4.297 | 4.781 |
| 10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 4.144 | 4.587 |
| 11 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 4.025 | 4.437 |
| 12 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 | 3.930 | 4.318 |
| 13 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 3.852 | 4.221 |
| 14 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 3.787 | 4.140 |
| 15 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 3.733 | 4.073 |
| 16 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 3.686 | 4.015 |
| 17 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.646 | 3.965 |
| 18 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.610 | 3.922 |
| 19 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.579 | 3.883 |
| 20 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.552 | 3.850 |
| 21 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 3.527 | 3.819 |
| 22 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.505 | 3.792 |
| 23 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.485 | 3.768 |
| 24 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.467 | 3.745 |
| 25 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 | 3.450 | 3.725 |
| 26 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.435 | 3.707 |
| 27 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.421 | 3.690 |
| 28 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.408 | 3.674 |
| 29 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.396 | 3.659 |
| 30 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.385 | 3.646 |
| 40 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 | 3.307 | 3.551 |
| 50 | 1.299 | 1.676 | 2.009 | 2.403 | 2.678 | 3.261 | 3.496 |
| 60 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 | 3.232 | 3.460 |
| 80 | 1.292 | 1.664 | 1.990 | 2.374 | 2.639 | 3.195 | 3.416 |
| 100 | 1.290 | 1.660 | 1.984 | 2.364 | 2.626 | 3.174 | 3.390 |
| 120 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 3.160 | 3.373 |
| 200 | 1.286 | 1.653 | 1.972 | 2.345 | 2.601 | 3.131 | 3.340 |
| 500 | 1.283 | 1.648 | 1.965 | 2.334 | 2.586 | 3.107 | 3.310 |
| 1000 | 1.282 | 1.646 | 1.962 | 2.330 | 2.581 | 3.098 | 3.300 |
| ∞ (z) | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 | 3.090 | 3.291 |
Frequently asked questions
- How do I find the critical value for a two-tailed test at 0.05?
- Use the column headed two-tailed 0.05 (one-tailed 0.025) and the row for your df. For df = 20 the value is 2.086.
- What if my degrees of freedom are not in the table?
- Type them into the lookup box for the exact value. Rounding down to the next listed df is acceptable in exams and gives a slightly conservative result.
- Why does the table end with the z values?
- As df grows the t distribution approaches the standard normal. The ∞ row shows the z critical values (1.960 for two-tailed 0.05) that the t values converge to.
- Is the t-table one-tailed or two-tailed?
- Both. Each column shows the one-tailed α and the corresponding two-tailed α, which is twice as large.
Last reviewed: September 25, 2026. Table values are generated from the same numerical routines as the calculators and were validated against SciPy.