Statistical tables

t Table: Critical Values of Student's t Distribution

Q: What is the critical t value for 95% confidence?

It depends on the degrees of freedom. For df = 10 it is 2.228, for df = 20 it is 2.086, for df = 30 it is 2.042, and for very large samples it approaches 1.960.

Q: What is the difference between one-tailed and two-tailed t values?

A two-tailed test splits α between both tails, so its critical value at α = .05 is the one-tailed value at α = .025. Use two-tailed unless you stated a directional hypothesis before collecting data.

Q: How do I calculate degrees of freedom for a t-test?

One-sample and paired t-tests: df = n − 1. Independent samples (equal variances): df = n₁ + n₂ − 2. Welch's t-test uses the Welch–Satterthwaite formula, which usually gives a non-integer df.

Q: Why does the t value get smaller as df increases?

With more data the sample standard deviation estimates the population value more precisely, so the t distribution has thinner tails and approaches the standard normal distribution.

Q: Is t = 2 significant?

Usually, if df is about 60 or more. The two-tailed .05 critical value is 2.000 at df = 60, 2.042 at df = 30 and 2.228 at df = 10, so with small samples t = 2 is not significant.

One- and two-tailed critical t values for degrees of freedom from 1 to ∞, with a calculator for any df and α and a p-value calculator for your t statistic.

df 1 to ∞α from .25 to .0005Printable

Critical values of Student's t distribution
1-tail α	0.25	0.1	0.05	0.025	0.01	0.005	0.0025	0.001	0.0005
2-tail α · df	0.5	0.2	0.1	0.05	0.02	0.01	0.005	0.002	0.001
1	1.000	3.078	6.314	12.706	31.821	63.657	127.321	318.309	636.619
2	0.816	1.886	2.920	4.303	6.965	9.925	14.089	22.327	31.599
3	0.765	1.638	2.353	3.182	4.541	5.841	7.453	10.215	12.924
4	0.741	1.533	2.132	2.776	3.747	4.604	5.598	7.173	8.610
5	0.727	1.476	2.015	2.571	3.365	4.032	4.773	5.893	6.869
6	0.718	1.440	1.943	2.447	3.143	3.707	4.317	5.208	5.959
7	0.711	1.415	1.895	2.365	2.998	3.499	4.029	4.785	5.408
8	0.706	1.397	1.860	2.306	2.896	3.355	3.833	4.501	5.041
9	0.703	1.383	1.833	2.262	2.821	3.250	3.690	4.297	4.781
10	0.700	1.372	1.812	2.228	2.764	3.169	3.581	4.144	4.587
11	0.697	1.363	1.796	2.201	2.718	3.106	3.497	4.025	4.437
12	0.695	1.356	1.782	2.179	2.681	3.055	3.428	3.930	4.318
13	0.694	1.350	1.771	2.160	2.650	3.012	3.372	3.852	4.221
14	0.692	1.345	1.761	2.145	2.624	2.977	3.326	3.787	4.140
15	0.691	1.341	1.753	2.131	2.602	2.947	3.286	3.733	4.073
16	0.690	1.337	1.746	2.120	2.583	2.921	3.252	3.686	4.015
17	0.689	1.333	1.740	2.110	2.567	2.898	3.222	3.646	3.965
18	0.688	1.330	1.734	2.101	2.552	2.878	3.197	3.610	3.922
19	0.688	1.328	1.729	2.093	2.539	2.861	3.174	3.579	3.883
20	0.687	1.325	1.725	2.086	2.528	2.845	3.153	3.552	3.850
21	0.686	1.323	1.721	2.080	2.518	2.831	3.135	3.527	3.819
22	0.686	1.321	1.717	2.074	2.508	2.819	3.119	3.505	3.792
23	0.685	1.319	1.714	2.069	2.500	2.807	3.104	3.485	3.768
24	0.685	1.318	1.711	2.064	2.492	2.797	3.091	3.467	3.745
25	0.684	1.316	1.708	2.060	2.485	2.787	3.078	3.450	3.725
26	0.684	1.315	1.706	2.056	2.479	2.779	3.067	3.435	3.707
27	0.684	1.314	1.703	2.052	2.473	2.771	3.057	3.421	3.690
28	0.683	1.313	1.701	2.048	2.467	2.763	3.047	3.408	3.674
29	0.683	1.311	1.699	2.045	2.462	2.756	3.038	3.396	3.659
30	0.683	1.310	1.697	2.042	2.457	2.750	3.030	3.385	3.646
35	0.682	1.306	1.690	2.030	2.438	2.724	2.996	3.340	3.591
40	0.681	1.303	1.684	2.021	2.423	2.704	2.971	3.307	3.551
45	0.680	1.301	1.679	2.014	2.412	2.690	2.952	3.281	3.520
50	0.679	1.299	1.676	2.009	2.403	2.678	2.937	3.261	3.496
60	0.679	1.296	1.671	2.000	2.390	2.660	2.915	3.232	3.460
70	0.678	1.294	1.667	1.994	2.381	2.648	2.899	3.211	3.435
80	0.678	1.292	1.664	1.990	2.374	2.639	2.887	3.195	3.416
90	0.677	1.291	1.662	1.987	2.368	2.632	2.878	3.183	3.402
100	0.677	1.290	1.660	1.984	2.364	2.626	2.871	3.174	3.390
120	0.677	1.289	1.658	1.980	2.358	2.617	2.860	3.160	3.373
150	0.676	1.287	1.655	1.976	2.351	2.609	2.849	3.145	3.357
200	0.676	1.286	1.653	1.972	2.345	2.601	2.839	3.131	3.340
500	0.675	1.283	1.648	1.965	2.334	2.586	2.820	3.107	3.310
1000	0.675	1.282	1.646	1.962	2.330	2.581	2.813	3.098	3.300
∞	0.674	1.282	1.645	1.960	2.326	2.576	2.807	3.090	3.291

Values computed with SciPy and checked against published tables. Free to use and print for teaching. Please link to this page if you share it.

How to read the t table

Find your degrees of freedom. For a one-sample or paired t-test, df = n − 1. For an independent samples t-test with equal variances, df = n₁ + n₂ − 2.
Pick the column for your α. Use the top header for a one-tailed test and the second header for a two-tailed test. Most research uses a two-tailed α = .05.
Compare. If the absolute value of your t statistic is larger than the table value, the result is statistically significant.

Worked example

A paired t-test on 21 students gives t = 2.45. Then df = 21 − 1 = 20. The two-tailed critical value at α = .05 is 2.086. Because 2.45 > 2.086, the difference is significant, p < .05. The exact p-value is .024, which the calculator on this page gives directly.

What if my df is not in the table?

Use the next smaller df in the table, which gives a slightly larger, more conservative critical value, or type your exact df into the calculator above. As df grows the t distribution approaches the normal distribution, which is why the ∞ row equals the z critical values (1.645, 1.960, 2.576).

Critical t for confidence intervals

For a 95% confidence interval use the two-tailed α = .05 column, for a 90% interval α = .10, and for a 99% interval α = .01. The interval is mean ± t_crit × SE.

Frequently asked questions

What is the critical t value for 95% confidence?

It depends on the degrees of freedom. For df = 10 it is 2.228, for df = 20 it is 2.086, for df = 30 it is 2.042, and for very large samples it approaches 1.960.

What is the difference between one-tailed and two-tailed t values?

A two-tailed test splits α between both tails, so its critical value at α = .05 is the one-tailed value at α = .025. Use two-tailed unless you stated a directional hypothesis before collecting data.

How do I calculate degrees of freedom for a t-test?

One-sample and paired t-tests: df = n − 1. Independent samples (equal variances): df = n₁ + n₂ − 2. Welch's t-test uses the Welch–Satterthwaite formula, which usually gives a non-integer df.

Why does the t value get smaller as df increases?

With more data the sample standard deviation estimates the population value more precisely, so the t distribution has thinner tails and approaches the standard normal distribution.

Is t = 2 significant?

Usually, if df is about 60 or more. The two-tailed .05 critical value is 2.000 at df = 60, 2.042 at df = 30 and 2.228 at df = 10, so with small samples t = 2 is not significant.

Run the test instead

You rarely need a table if you run the test in software, because the exact p-value is reported. These free tools give the t statistic, df, p-value, effect size and an APA write-up: