Statistics Reference

T-Table for α = 0.025 (t Critical Values)

Student's t critical values at the 0.025 level for every degree of freedom from 1 to 100 (plus the large-sample tail). The one-tail column doubles as the multiplier for 95% confidence intervals — the most-quoted t values in statistics — while the two-tail column serves 97.5% intervals and 2.5% two-sided tests.

How to Read This Table

Rows are degrees of freedom — every integer from 1 to 100, then 120, 150, 200, 500, and 1000, finer than the stepped rows of the main table. The one-tail column puts all of α = 0.025 in a single tail (directional tests); the two-tail column splits it across both tails (non-directional tests and confidence intervals). The distribution is symmetric, so lower-tail tests use the negative of the printed value.

95% confidence interval from a sample of 21 (df = 20):

Row df = 20, one-tail column: 2.086 — the familiar 95% CI multiplier.
Interval: sample mean ± 2.086 standard errors.
The identity: one-tail 0.025 = two-tail 0.05, because 2.5% per tail sums to 5%.

Common uses of this level:

The one-tail 0.025 values are the 95% CI multipliers (identical to two-tail 0.05)
Directional tests at the 2.5% significance level
97.5% confidence intervals (two-tail column)

t Critical Values, α = 0.025, df 1–1000

Student's t critical values at significance level 0.025 for degrees of freedom 1 to 1000
df	One-tail α = 0.025	Two-tail α = 0.025
1	12.706	25.452
2	4.303	6.205
3	3.182	4.177
4	2.776	3.495
5	2.571	3.163
6	2.447	2.969
7	2.365	2.841
8	2.306	2.752
9	2.262	2.685
10	2.228	2.634
11	2.201	2.593
12	2.179	2.560
13	2.160	2.533
14	2.145	2.510
15	2.131	2.490
16	2.120	2.473
17	2.110	2.458
18	2.101	2.445
19	2.093	2.433
20	2.086	2.423
21	2.080	2.414
22	2.074	2.405
23	2.069	2.398
24	2.064	2.391
25	2.060	2.385
26	2.056	2.379
27	2.052	2.373
28	2.048	2.368
29	2.045	2.364
30	2.042	2.360
31	2.040	2.356
32	2.037	2.352
33	2.035	2.348
34	2.032	2.345
35	2.030	2.342
36	2.028	2.339
37	2.026	2.336
38	2.024	2.334
39	2.023	2.331
40	2.021	2.329
41	2.020	2.327
42	2.018	2.325
43	2.017	2.323
44	2.015	2.321
45	2.014	2.319
46	2.013	2.317
47	2.012	2.315
48	2.011	2.314
49	2.010	2.312
50	2.009	2.311
51	2.008	2.310
52	2.007	2.308
53	2.006	2.307
54	2.005	2.306
55	2.004	2.304
56	2.003	2.303
57	2.002	2.302
58	2.002	2.301
59	2.001	2.300
60	2.000	2.299
61	2.000	2.298
62	1.999	2.297
63	1.998	2.296
64	1.998	2.295
65	1.997	2.295
66	1.997	2.294
67	1.996	2.293
68	1.995	2.292
69	1.995	2.291
70	1.994	2.291
71	1.994	2.290
72	1.993	2.289
73	1.993	2.289
74	1.993	2.288
75	1.992	2.287
76	1.992	2.287
77	1.991	2.286
78	1.991	2.285
79	1.990	2.285
80	1.990	2.284
81	1.990	2.284
82	1.989	2.283
83	1.989	2.283
84	1.989	2.282
85	1.988	2.282
86	1.988	2.281
87	1.988	2.281
88	1.987	2.280
89	1.987	2.280
90	1.987	2.280
91	1.986	2.279
92	1.986	2.279
93	1.986	2.278
94	1.986	2.278
95	1.985	2.277
96	1.985	2.277
97	1.985	2.277
98	1.984	2.276
99	1.984	2.276
100	1.984	2.276
120	1.980	2.270
150	1.976	2.264
200	1.972	2.258
500	1.965	2.248
1000	1.962	2.245

Other Significance Levels

The t-table overview carries the classic multi-column grid, degrees-of-freedom rules, and the z-convergence walkthrough. The other levels each have a dedicated page:

Frequently Asked Questions

Why do 95% confidence intervals use the 0.025 column?

A 95% interval leaves 5% of probability split across two tails - 2.5% each. The critical value that cuts 2.5% from one tail is therefore the interval's multiplier. That is why this page's one-tail column contains the most-quoted t values in applied statistics: 2.228 at df = 10, 2.086 at df = 20, 1.984 at df = 100.

Is the one-tail 0.025 column the same as a two-tail 0.05 column?

Identical, cell for cell - one-tail α = 0.025 and two-tail α = 0.05 describe the same cutoff from two viewpoints. Tables differ only in which label they print. This page also provides the genuine two-tail 0.025 column (2.5% split as 1.25% per tail) for 97.5% intervals.

When would I run a test at α = 0.025 rather than 0.05?

Mostly in one-sided settings where the two-sided convention is 5%: regulatory and clinical frameworks often require one-sided tests at 2.5% so that the directional claim carries the same evidentiary weight as the standard two-sided test. It also appears as the per-side level inside 95% two-sided procedures.