Table 9.10.4: 0.95 and 0.975 Fractilesa of the t Distribution Associated with df Degrees of Freedom

MIL-HDBK-5J, Metallic Materials and Elements for Aerospace Vehicle Structures

Last Updated 29 Oct 2026

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df	t_.95	t_.975	df	t_.95	t_.975
1	6.314	12.706	21	1.721	2.080
2	2.920	4.303	22	1.717	2.074
3	2.353	3.182	23	1.714	2.069
4	2.132	2.776	24	1.711	2.064
5	2.015	2.571	25	1.708	2.060
6	1.943	2.447	26	1.706	2.056
7	1.895	2.365	27	1.703	2.052
8	1.860	2.306	28	1.701	2.048
9	1.833	2.262	29	1.699	2.045
10	1.812	2.228	30	1.697	2.042
11	1.796	2.201	40	1.684	2.021
12	1.782	2.179	50	1.676	2.009
13	1.771	2.160	60	1.671	2.000
14	1.761	2.145	80	1.664	1.990
15	1.753	2.131	100	1.660	1.984
16	1.746	2.120	120	1.658	1.980
17	1.740	2.110	200	1.653	1.972
18	1.734	2.101	500	1.648	1.965
19	1.729	2.093	∞	1.645	1.960
20	1.725	2.086

a The following equations may be used to compute 0.95 and 0.975 fractiles of the t distribution in lieu of using table values:

$\begin{aligned} t_{.95} & \approx 1.645+\exp [0.377-0.990 \ln (\gamma)+1.15 / \gamma] \\ t_{.975} & \approx 1.96+\exp [0.779-0.980 \ln (\gamma)+1.57 / \gamma]\end{aligned}$

where $\gamma$ is the degrees of freedom (df). These approximations are accurate to within $0.5 \%$ for $\gamma \geq 4$ .

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