t-distribution table (two-tailed)

This table lists critical values of the t-distribution. These critical t-values are used to determine the threshold for significance in various statistical tests and to establish the upper and lower bounds of confidence intervals (see example below the table).

t-distribution.

DF	0.80 0.20	0.90 0.10	0.95 0.05	0.98 0.02	0.99 0.01	0.995 0.005	0.998 0.002	0.999 0.001
1	3.078	6.314	12.706	31.820	63.657	127.321	318.309	636.619
2	1.886	2.920	4.303	6.965	9.925	14.089	22.327	31.599
3	1.638	2.353	3.182	4.541	5.841	7.453	10.215	12.924
4	1.533	2.132	2.776	3.747	4.604	5.598	7.173	8.610
5	1.476	2.015	2.571	3.365	4.032	4.773	5.893	6.869
6	1.440	1.943	2.447	3.143	3.707	4.317	5.208	5.959
7	1.415	1.895	2.365	2.998	3.499	4.029	4.785	5.408
8	1.397	1.860	2.306	2.897	3.355	3.833	4.501	5.041
9	1.383	1.833	2.262	2.821	3.250	3.690	4.297	4.781
10	1.372	1.812	2.228	2.764	3.169	3.581	4.144	4.587
11	1.363	1.796	2.201	2.718	3.106	3.497	4.025	4.437
12	1.356	1.782	2.179	2.681	3.055	3.428	3.930	4.318
13	1.350	1.771	2.160	2.650	3.012	3.372	3.852	4.221
14	1.345	1.761	2.145	2.625	2.977	3.326	3.787	4.140
15	1.341	1.753	2.131	2.602	2.947	3.286	3.733	4.073
16	1.337	1.746	2.120	2.584	2.921	3.252	3.686	4.015
17	1.333	1.740	2.110	2.567	2.898	3.222	3.646	3.965
18	1.330	1.734	2.101	2.552	2.878	3.197	3.610	3.922
19	1.328	1.729	2.093	2.539	2.861	3.174	3.579	3.883
20	1.325	1.725	2.086	2.528	2.845	3.153	3.552	3.850
21	1.323	1.721	2.080	2.518	2.831	3.135	3.527	3.819
22	1.321	1.717	2.074	2.508	2.819	3.119	3.505	3.792
23	1.319	1.714	2.069	2.500	2.807	3.104	3.485	3.768
24	1.318	1.711	2.064	2.492	2.797	3.090	3.467	3.745
25	1.316	1.708	2.060	2.485	2.787	3.078	3.450	3.725
26	1.315	1.706	2.056	2.479	2.779	3.067	3.435	3.707
27	1.314	1.703	2.052	2.473	2.771	3.057	3.421	3.690
28	1.313	1.701	2.048	2.467	2.763	3.047	3.408	3.674
29	1.311	1.699	2.045	2.462	2.756	3.038	3.396	3.659
30	1.310	1.697	2.042	2.457	2.750	3.030	3.385	3.646
31	1.309	1.695	2.040	2.453	2.744	3.022	3.375	3.633
32	1.309	1.694	2.037	2.449	2.738	3.015	3.365	3.622
33	1.308	1.692	2.035	2.445	2.733	3.008	3.356	3.611
34	1.307	1.691	2.032	2.441	2.728	3.002	3.348	3.601
35	1.306	1.690	2.030	2.438	2.724	2.996	3.340	3.591
36	1.306	1.688	2.028	2.434	2.719	2.991	3.333	3.582
37	1.305	1.687	2.026	2.431	2.715	2.985	3.326	3.574
38	1.304	1.686	2.024	2.429	2.712	2.980	3.319	3.566
39	1.304	1.685	2.023	2.426	2.708	2.976	3.313	3.558
40	1.303	1.684	2.021	2.423	2.704	2.971	3.307	3.551
42	1.302	1.682	2.018	2.418	2.698	2.963	3.296	3.538
44	1.301	1.680	2.015	2.414	2.692	2.956	3.286	3.526
46	1.300	1.679	2.013	2.410	2.687	2.949	3.277	3.515
48	1.299	1.677	2.011	2.407	2.682	2.943	3.269	3.505
50	1.299	1.676	2.009	2.403	2.678	2.937	3.261	3.496
60	1.296	1.671	2.000	2.390	2.660	2.915	3.232	3.460
70	1.294	1.667	1.994	2.381	2.648	2.899	3.211	3.435
80	1.292	1.664	1.990	2.374	2.639	2.887	3.195	3.416
90	1.291	1.662	1.987	2.369	2.632	2.878	3.183	3.402
100	1.290	1.660	1.984	2.364	2.626	2.871	3.174	3.391
120	1.289	1.658	1.980	2.358	2.617	2.860	3.160	3.373
150	1.287	1.655	1.976	2.351	2.609	2.849	3.145	3.357
200	1.286	1.652	1.972	2.345	2.601	2.839	3.131	3.340
300	1.284	1.650	1.968	2.339	2.592	2.828	3.118	3.323
500	1.283	1.648	1.965	2.334	2.586	2.820	3.107	3.310
∞	1.282	1.645	1.960	2.326	2.576	2.807	3.090	3.291

Example: establish the upper and lower bounds of a confidence interval of a mean

The mean of a sample is 128.5, the standard error of the mean (SEM) is 6.2, and the sample size is 32.

What is the 99% confidence interval of the mean?

The degrees of freedom (DF) is n−1 = 31, the t-value in the column for area 0.99 is 2.744. The 99% CI therefore is:

mean − t SEM	to	mean + t SEM
128.5 − 2.744 × 6.2	to	128.5 + 2.744 × 6.2
111.5	to	145.5

t-distribution table (two-tailed)

Example: establish the upper and lower bounds of a confidence interval of a mean

See also