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t-distribution table

Critical values of Student's t. Column headings are the area in the upper tail (one-tailed α); the two-tailed α is twice that.

Look up any df

Degrees of freedom

Alpha (α)

Tails

Or: your t statistic

Download the printable t table (PDF, 1 page) →

Critical values of t

df \ one-tail α	0.1	0.05	0.025	0.01	0.005	0.001
two-tail α	0.2	0.1	0.05	0.02	0.01	0.002
1	3.078	6.314	12.706	31.821	63.657	318.309
2	1.886	2.920	4.303	6.965	9.925	22.327
3	1.638	2.353	3.182	4.541	5.841	10.215
4	1.533	2.132	2.776	3.747	4.604	7.173
5	1.476	2.015	2.571	3.365	4.032	5.893
6	1.440	1.943	2.447	3.143	3.707	5.208
7	1.415	1.895	2.365	2.998	3.499	4.785
8	1.397	1.860	2.306	2.896	3.355	4.501
9	1.383	1.833	2.262	2.821	3.250	4.297
10	1.372	1.812	2.228	2.764	3.169	4.144
11	1.363	1.796	2.201	2.718	3.106	4.025
12	1.356	1.782	2.179	2.681	3.055	3.930
13	1.350	1.771	2.160	2.650	3.012	3.852
14	1.345	1.761	2.145	2.624	2.977	3.787
15	1.341	1.753	2.131	2.602	2.947	3.733
16	1.337	1.746	2.120	2.583	2.921	3.686
17	1.333	1.740	2.110	2.567	2.898	3.646
18	1.330	1.734	2.101	2.552	2.878	3.610
19	1.328	1.729	2.093	2.539	2.861	3.579
20	1.325	1.725	2.086	2.528	2.845	3.552
21	1.323	1.721	2.080	2.518	2.831	3.527
22	1.321	1.717	2.074	2.508	2.819	3.505
23	1.319	1.714	2.069	2.500	2.807	3.485
24	1.318	1.711	2.064	2.492	2.797	3.467
25	1.316	1.708	2.060	2.485	2.787	3.450
26	1.315	1.706	2.056	2.479	2.779	3.435
27	1.314	1.703	2.052	2.473	2.771	3.421
28	1.313	1.701	2.048	2.467	2.763	3.408
29	1.311	1.699	2.045	2.462	2.756	3.396
30	1.310	1.697	2.042	2.457	2.750	3.385
40	1.303	1.684	2.021	2.423	2.704	3.307
50	1.299	1.676	2.009	2.403	2.678	3.261
60	1.296	1.671	2.000	2.390	2.660	3.232
80	1.292	1.664	1.990	2.374	2.639	3.195
100	1.290	1.660	1.984	2.364	2.626	3.174
120	1.289	1.658	1.980	2.358	2.617	3.160
∞ (z)	1.282	1.645	1.960	2.326	2.576	3.090

Computed from the t distribution (regularized incomplete beta function) and checked against published tables in our test suite.

Use it with: t-test calculator · Confidence intervals · Which hypothesis test to use

FAQ

How do I read a t table?

Pick the row for your degrees of freedom and the column for your alpha. For a two-tailed test at α = 0.05, use the 0.025 one-tail column (the two-tail 0.05 heading), because α is split between the two tails.

What degrees of freedom do I use?

n − 1 for a one-sample or paired t-test, n₁ + n₂ − 2 for a pooled two-sample test, and the Welch–Satterthwaite value for unequal variances. For a regression coefficient, n minus the number of estimated parameters.

My df is not in the table. What do I do?

Use the calculator above, which works for any df. If you are using the printed table in an exam, take the next lower df row: it gives a slightly larger critical value, which is the conservative choice.

Why does the last row match the z table?

As df grows, the t distribution approaches the standard normal. At infinite df the critical values are the z values: 1.645, 1.960, 2.326 and 2.576.

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