Student's t-Distribution Table

Critical t-values for common significance levels and degrees of freedom. Find the value where your row (df) meets your column (tail probability).

Critical t-values. Column headers show one-tailed α (two-tailed α below).

df	0.1002-tail 0.20	0.0502-tail 0.10	0.0252-tail 0.05	0.0102-tail 0.02	0.0052-tail 0.01
1	3.078	6.314	12.706	31.821	63.657
2	1.886	2.920	4.303	6.965	9.925
3	1.638	2.353	3.182	4.541	5.841
4	1.533	2.132	2.776	3.747	4.604
5	1.476	2.015	2.571	3.365	4.032
6	1.440	1.943	2.447	3.143	3.707
7	1.415	1.895	2.365	2.998	3.499
8	1.397	1.860	2.306	2.896	3.355
9	1.383	1.833	2.262	2.821	3.250
10	1.372	1.812	2.228	2.764	3.169
11	1.363	1.796	2.201	2.718	3.106
12	1.356	1.782	2.179	2.681	3.055
13	1.350	1.771	2.160	2.650	3.012
14	1.345	1.761	2.145	2.624	2.977
15	1.341	1.753	2.131	2.602	2.947
16	1.337	1.746	2.120	2.583	2.921
17	1.333	1.740	2.110	2.567	2.898
18	1.330	1.734	2.101	2.552	2.878
19	1.328	1.729	2.093	2.539	2.861
20	1.325	1.725	2.086	2.528	2.845
21	1.323	1.721	2.080	2.518	2.831
22	1.321	1.717	2.074	2.508	2.819
23	1.319	1.714	2.069	2.500	2.807
24	1.318	1.711	2.064	2.492	2.797
25	1.316	1.708	2.060	2.485	2.787
26	1.315	1.706	2.056	2.479	2.779
27	1.314	1.703	2.052	2.473	2.771
28	1.313	1.701	2.048	2.467	2.763
29	1.311	1.699	2.045	2.462	2.756
30	1.310	1.697	2.042	2.457	2.750
40	1.303	1.684	2.021	2.423	2.704
60	1.296	1.671	2.000	2.390	2.660
80	1.292	1.664	1.990	2.374	2.639
100	1.290	1.660	1.984	2.364	2.626
∞	1.282	1.646	1.962	2.330	2.581

How to read the t table

Find your degrees of freedom (df) in the left column — usually the sample size minus one.
Pick the column for your significance level. The top number is the one-tailed α; the smaller line below is the equivalent two-tailed α.
The cell where they meet is the critical t-value. Reject the null hypothesis if your test statistic is more extreme than this value.

About the t-distribution

The t-distribution is bell-shaped like the normal distribution but has heavier tails, which account for the extra uncertainty of estimating the standard deviation from a small sample. As the degrees of freedom increase, the t-distribution approaches the standard normal, so the last row (∞) matches the z critical values.

Frequently asked questions

What is the t critical value for a 95% confidence interval?

For a 95% confidence interval you use the two-tailed α = 0.05 column (one-tailed 0.025). For example, with 10 degrees of freedom the critical t-value is about 2.228.

How do I find degrees of freedom for the t table?

For a one-sample t-test or confidence interval, the degrees of freedom equal the sample size minus one (n − 1). Other tests, such as two-sample tests, use different formulas.

Related calculators

P-Value

Confidence Interval

Hypothesis Test