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t-table (critical values of the t distribution)

Critical values of Student’s t for every common significance level — and an exact lookup for the dfs printed tables skip. Computed from the same distribution code our statistics engine uses.

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Exact t lookup

Any df (including fractional Welch df) and any α — exact values, not the nearest printed row.

Significance level

Degrees of freedom (df)

t value (optional)

Critical values of t

Two-tailed significance level across the top (halve it for a one-tailed test: the α = .05 two-tailed column is the α = .025 one-tailed column).

df	α = .2	α = .1	α = .05	α = .02	α = .01	α = .001
1	3.078	6.314	12.706	31.821	63.657	636.619
2	1.886	2.920	4.303	6.965	9.925	31.599
3	1.638	2.353	3.182	4.541	5.841	12.924
4	1.533	2.132	2.776	3.747	4.604	8.610
5	1.476	2.015	2.571	3.365	4.032	6.869
6	1.440	1.943	2.447	3.143	3.707	5.959
7	1.415	1.895	2.365	2.998	3.499	5.408
8	1.397	1.860	2.306	2.896	3.355	5.041
9	1.383	1.833	2.262	2.821	3.250	4.781
10	1.372	1.812	2.228	2.764	3.169	4.587
11	1.363	1.796	2.201	2.718	3.106	4.437
12	1.356	1.782	2.179	2.681	3.055	4.318
13	1.350	1.771	2.160	2.650	3.012	4.221
14	1.345	1.761	2.145	2.624	2.977	4.140
15	1.341	1.753	2.131	2.602	2.947	4.073
16	1.337	1.746	2.120	2.583	2.921	4.015
17	1.333	1.740	2.110	2.567	2.898	3.965
18	1.330	1.734	2.101	2.552	2.878	3.922
19	1.328	1.729	2.093	2.539	2.861	3.883
20	1.325	1.725	2.086	2.528	2.845	3.850
21	1.323	1.721	2.080	2.518	2.831	3.819
22	1.321	1.717	2.074	2.508	2.819	3.792
23	1.319	1.714	2.069	2.500	2.807	3.768
24	1.318	1.711	2.064	2.492	2.797	3.745
25	1.316	1.708	2.060	2.485	2.787	3.725
26	1.315	1.706	2.056	2.479	2.779	3.707
27	1.314	1.703	2.052	2.473	2.771	3.690
28	1.313	1.701	2.048	2.467	2.763	3.674
29	1.311	1.699	2.045	2.462	2.756	3.659
30	1.310	1.697	2.042	2.457	2.750	3.646
40	1.303	1.684	2.021	2.423	2.704	3.551
60	1.296	1.671	2.000	2.390	2.660	3.460
120	1.289	1.658	1.980	2.358	2.617	3.373
∞ (z)	1.282	1.645	1.960	2.326	2.576	3.291

Reject H0 when |t| exceeds the table value. df = n − 1 for one sample or paired data; df = n1 + n2 − 2 for two independent groups (pooled).

How to read the table

Find your degrees of freedom in the left column and your significance level across the top. The cell is the critical value: if your computed |t| is larger, the result is significant at that level. Example: a two-sample study with 15 participants per group has df = 28; at α = .05 (two-tailed) the critical value is 2.048, so t = 2.31 is significant while t = 1.90 is not.

For a one-tailed test, use the column for twice your α (a one-tailed test at .05 uses the two-tailed .10 column: 1.701 at df = 28). One-tailed tests are only defensible when the direction was fixed in advance.

The same values build confidence intervals: M ± t(α, df) × SE. As df grows, t approaches z — by df = 120 the .05 critical value is 1.980, barely above the normal 1.960, which is why "±2 standard errors" works as a mental shortcut.

Frequently asked questions

What are degrees of freedom and which do I use?

Degrees of freedom count the independent pieces of information behind your variance estimate. One-sample or paired t-test: df = n − 1. Independent samples (pooled): df = n1 + n2 − 2. Welch’s t-test uses a fractional df printed by your software — use the exact lookup above for those.

My df is not in the table — what now?

Use the exact lookup at the top of this page — it accepts any df, including fractional Welch dfs. If you must use the printed table, take the next SMALLER df (more conservative).

Why is t at df = 1 so huge (12.706)?

With a single degree of freedom, the SD estimate is extremely unstable, so the t distribution has very heavy tails and demands an enormous statistic before calling anything significant. It is a built-in penalty for tiny samples — and a reminder that n = 2 rarely proves anything.

Related free tools

Sample size calculator Sample size for two groups Effect size (Cohen's d)Descriptive statistics One-sample t-test Independent t-test Paired t-test z-table (standard normal)Chi-square table F-table (ANOVA)

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