Student's t Critical Values Table

Q: What are degrees of freedom in the t-table?

For a one-sample t-test, df = n − 1 where n is the sample size. For a two-sample t-test, df depends on the pooled or Welch approximation.

Q: How do I use this for a one-tailed test?

For a one-tailed test at significance α, look up the column 2α (since this table uses two-tailed α). For example, one-tailed α = 0.05 corresponds to two-tailed α = 0.10.

The Student's t table shows critical values t* for two-tailed hypothesis tests. For a given degrees of freedom (df) and significance level α, the cell gives the value t* where P(|T| > t*) = α.

These values are essential for t-tests, confidence intervals with small samples, and regression analysis. Hover a cell to see the rejection regions on the companion chart.

df \ α (two-tailed)	0.1	0.05	0.025	0.01	0.005
1	6.3138	12.7062	25.4517	63.6567	127.3213
2	2.9200	4.3027	6.2053	9.9248	14.0890
3	2.3534	3.1824	4.1765	5.8409	7.4533
4	2.1318	2.7764	3.4954	4.6041	5.5976
5	2.0150	2.5706	3.1634	4.0321	4.7733
6	1.9432	2.4469	2.9687	3.7074	4.3168
7	1.8946	2.3646	2.8412	3.4995	4.0293
8	1.8595	2.3060	2.7515	3.3554	3.8325
9	1.8331	2.2622	2.6850	3.2498	3.6897
10	1.8125	2.2281	2.6338	3.1693	3.5814
11	1.7959	2.2010	2.5931	3.1058	3.4966
12	1.7823	2.1788	2.5600	3.0545	3.4284
13	1.7709	2.1604	2.5326	3.0123	3.3725
14	1.7613	2.1448	2.5096	2.9768	3.3257
15	1.7531	2.1314	2.4899	2.9467	3.2860
16	1.7459	2.1199	2.4729	2.9208	3.2520
17	1.7396	2.1098	2.4581	2.8982	3.2224
18	1.7341	2.1009	2.4450	2.8784	3.1966
19	1.7291	2.0930	2.4334	2.8609	3.1737
20	1.7247	2.0860	2.4231	2.8453	3.1534
21	1.7207	2.0796	2.4138	2.8314	3.1352
22	1.7171	2.0739	2.4055	2.8188	3.1188
23	1.7139	2.0687	2.3979	2.8073	3.1040
24	1.7109	2.0639	2.3909	2.7969	3.0905
25	1.7081	2.0595	2.3846	2.7874	3.0782
26	1.7056	2.0555	2.3788	2.7787	3.0669
27	1.7033	2.0518	2.3734	2.7707	3.0565
28	1.7011	2.0484	2.3685	2.7633	3.0469
29	1.6991	2.0452	2.3638	2.7564	3.0380
30	1.6973	2.0423	2.3596	2.7500	3.0298
40	1.6839	2.0211	2.3289	2.7045	2.9712
60	1.6706	2.0003	2.2990	2.6603	2.9146
80	1.6641	1.9901	2.2844	2.6387	2.8870
100	1.6602	1.9840	2.2757	2.6259	2.8707
120	1.6577	1.9799	2.2699	2.6174	2.8599

Distribution Curve

How to Use

Find the row for your degrees of freedom (df = n − 1)
Find the column for your significance level α
The cell gives t* for a two-tailed test: reject H₀ if |t| > t*
For one-tailed: use column 2α (e.g., one-tailed 0.05 → column 0.1)

Explore this distribution interactively:

Open Student's Distribution →

Frequently Asked Questions

When should I use the t-table instead of the Z-table?

Use the t-table when the population standard deviation is unknown and estimated from the sample, especially with small samples (n < 30). As df increases, t converges to Z.

What are degrees of freedom in the t-table?

For a one-sample t-test, df = n − 1 where n is the sample size. For a two-sample t-test, df depends on the pooled or Welch approximation.

How do I use this for a one-tailed test?

For a one-tailed test at significance α, look up the column 2α (since this table uses two-tailed α). For example, one-tailed α = 0.05 corresponds to two-tailed α = 0.10.