Statistical Tables · free & public domain

t-Distribution Table (Critical Values)

Critical values of Student’s t by degrees of freedom, for one- and two-tailed tests.

How to use this table

Work out your degrees of freedom first (d.f. = n − 1 for a one-sample test). Read down to that d.f., then across to your α — use the one-tail row for a directional hypothesis, the two-tail row otherwise. Reject H₀ if |t| exceeds the value. Example: n = 20, two-tailed α = 0.05 → d.f. = 19, column 0.025 → 2.093.

The table

t-Distribution Table (Critical Values)
two-tail α	0.50	0.20	0.10	0.05	0.02	0.01	0.002
d.f. / one-tail α	0.25	0.1	0.05	0.025	0.01	0.005	0.001
1	1.000	3.078	6.314	12.706	31.821	63.657	318.309
2	0.816	1.886	2.920	4.303	6.965	9.925	22.327
3	0.765	1.638	2.353	3.182	4.541	5.841	10.215
4	0.741	1.533	2.132	2.776	3.747	4.604	7.173
5	0.727	1.476	2.015	2.571	3.365	4.032	5.893
6	0.718	1.440	1.943	2.447	3.143	3.707	5.208
7	0.711	1.415	1.895	2.365	2.998	3.499	4.785
8	0.706	1.397	1.860	2.306	2.896	3.355	4.501
9	0.703	1.383	1.833	2.262	2.821	3.250	4.297
10	0.700	1.372	1.812	2.228	2.764	3.169	4.144
11	0.697	1.363	1.796	2.201	2.718	3.106	4.025
12	0.695	1.356	1.782	2.179	2.681	3.055	3.930
13	0.694	1.350	1.771	2.160	2.650	3.012	3.852
14	0.692	1.345	1.761	2.145	2.624	2.977	3.787
15	0.691	1.341	1.753	2.131	2.602	2.947	3.733
16	0.690	1.337	1.746	2.120	2.583	2.921	3.686
17	0.689	1.333	1.740	2.110	2.567	2.898	3.646
18	0.688	1.330	1.734	2.101	2.552	2.878	3.610
19	0.688	1.328	1.729	2.093	2.539	2.861	3.579
20	0.687	1.325	1.725	2.086	2.528	2.845	3.552
21	0.686	1.323	1.721	2.080	2.518	2.831	3.527
22	0.686	1.321	1.717	2.074	2.508	2.819	3.505
23	0.685	1.319	1.714	2.069	2.500	2.807	3.485
24	0.685	1.318	1.711	2.064	2.492	2.797	3.467
25	0.684	1.316	1.708	2.060	2.485	2.787	3.450
26	0.684	1.315	1.706	2.056	2.479	2.779	3.435
27	0.684	1.314	1.703	2.052	2.473	2.771	3.421
28	0.683	1.313	1.701	2.048	2.467	2.763	3.408
29	0.683	1.311	1.699	2.045	2.462	2.756	3.396
30	0.683	1.310	1.697	2.042	2.457	2.750	3.385
32	0.682	1.309	1.694	2.037	2.449	2.738	3.365
34	0.682	1.307	1.691	2.032	2.441	2.728	3.348
36	0.681	1.306	1.688	2.028	2.434	2.719	3.333
38	0.681	1.304	1.686	2.024	2.429	2.712	3.319
40	0.681	1.303	1.684	2.021	2.423	2.704	3.307
45	0.680	1.301	1.679	2.014	2.412	2.690	3.281
50	0.679	1.299	1.676	2.009	2.403	2.678	3.261
60	0.679	1.296	1.671	2.000	2.390	2.660	3.232
70	0.678	1.294	1.667	1.994	2.381	2.648	3.211
80	0.678	1.292	1.664	1.990	2.374	2.639	3.195
90	0.677	1.291	1.662	1.987	2.368	2.632	3.183
100	0.677	1.290	1.660	1.984	2.364	2.626	3.174
120	0.677	1.289	1.658	1.980	2.358	2.617	3.160
150	0.676	1.287	1.655	1.976	2.351	2.609	3.145
200	0.676	1.286	1.653	1.972	2.345	2.601	3.131
300	0.675	1.284	1.650	1.968	2.339	2.592	3.118
500	0.675	1.283	1.648	1.965	2.334	2.586	3.107
1000	0.675	1.282	1.646	1.962	2.330	2.581	3.098
∞ (z)	0.674	1.282	1.645	1.960	2.326	2.576	3.090

Includes a 0.001 one-tail column and d.f. out to 1000, both beyond the usual printed range.

How these values were produced

Inverse survival function of Student’s t (SciPy 1.17). Distribution first published by W. S. Gosset, writing as “Student”: Student (1908), Biometrika 6(1), 1–25.

Every one of these 343 values was computed from the underlying distribution — none was transcribed from a printed table. Values of this kind are mathematical facts: they come out the same for anyone who computes them correctly.

Need the test run rather than the critical value looked up? The Proof Workbench computes t, r, χ² and ANOVA in your browser with assumption checks and a re-verifiable receipt.

Use it freely

This table is dedicated to the public domain under CC0 1.0. No attribution required, no signup, no limits — copy it into a lecture, a textbook, or your own site. A link back is welcome but not asked for.

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