Student's t Distribution Table: Critical Values

How to read the table: each column is a significance level α and each row a degrees of freedom ν. The same critical t value works for two cases depending on the test:

One-tailed test: leaves an area α in the right tail, P(T > t) = α. Use the "1 tail" row.
Two-tailed test: leaves an area α split between both tails, P(|T| > t) = α. Use the "2 tails" row.

Since the two tails split the area, always α (2 tails) = 2 × α (1 tail). Example: with ν = 10, for a two-tailed test at 5% (column "2 tails: 0.05" ↔ "1 tail: 0.025") the critical value is t = 2.228.

Click a cell to read the critical value.

ν (df)	Significance level α (tail area)
ν (df)	1 tail: 0.25 2 tails: 0.5	1 tail: 0.2 2 tails: 0.4	1 tail: 0.15 2 tails: 0.3	1 tail: 0.1 2 tails: 0.2	1 tail: 0.05 2 tails: 0.1	1 tail: 0.025 2 tails: 0.05	1 tail: 0.01 2 tails: 0.02	1 tail: 0.005 2 tails: 0.01	1 tail: 0.001 2 tails: 0.002
1	1.000	1.376	1.963	3.078	6.314	12.706	31.821	63.657	318.309
2	0.816	1.061	1.386	1.886	2.920	4.303	6.965	9.925	22.327
3	0.765	0.978	1.250	1.638	2.353	3.182	4.541	5.841	10.215
4	0.741	0.941	1.190	1.533	2.132	2.776	3.747	4.604	7.173
5	0.727	0.920	1.156	1.476	2.015	2.571	3.365	4.032	5.893
6	0.718	0.906	1.134	1.440	1.943	2.447	3.143	3.707	5.208
7	0.711	0.896	1.119	1.415	1.895	2.365	2.998	3.499	4.785
8	0.706	0.889	1.108	1.397	1.860	2.306	2.896	3.355	4.501
9	0.703	0.883	1.100	1.383	1.833	2.262	2.821	3.250	4.297
10	0.700	0.879	1.093	1.372	1.812	2.228	2.764	3.169	4.144
11	0.697	0.876	1.088	1.363	1.796	2.201	2.718	3.106	4.025
12	0.695	0.873	1.083	1.356	1.782	2.179	2.681	3.055	3.930
13	0.694	0.870	1.079	1.350	1.771	2.160	2.650	3.012	3.852
14	0.692	0.868	1.076	1.345	1.761	2.145	2.624	2.977	3.787
15	0.691	0.866	1.074	1.341	1.753	2.131	2.602	2.947	3.733
16	0.690	0.865	1.071	1.337	1.746	2.120	2.583	2.921	3.686
17	0.689	0.863	1.069	1.333	1.740	2.110	2.567	2.898	3.646
18	0.688	0.862	1.067	1.330	1.734	2.101	2.552	2.878	3.610
19	0.688	0.861	1.066	1.328	1.729	2.093	2.539	2.861	3.579
20	0.687	0.860	1.064	1.325	1.725	2.086	2.528	2.845	3.552
21	0.686	0.859	1.063	1.323	1.721	2.080	2.518	2.831	3.527
22	0.686	0.858	1.061	1.321	1.717	2.074	2.508	2.819	3.505
23	0.685	0.858	1.060	1.319	1.714	2.069	2.500	2.807	3.485
24	0.685	0.857	1.059	1.318	1.711	2.064	2.492	2.797	3.467
25	0.684	0.856	1.058	1.316	1.708	2.060	2.485	2.787	3.450
26	0.684	0.856	1.058	1.315	1.706	2.056	2.479	2.779	3.435
27	0.684	0.855	1.057	1.314	1.703	2.052	2.473	2.771	3.421
28	0.683	0.855	1.056	1.313	1.701	2.048	2.467	2.763	3.408
29	0.683	0.854	1.055	1.311	1.699	2.045	2.462	2.756	3.396
30	0.683	0.854	1.055	1.310	1.697	2.042	2.457	2.750	3.385
35	0.682	0.852	1.052	1.306	1.690	2.030	2.438	2.724	3.340
40	0.681	0.851	1.050	1.303	1.684	2.021	2.423	2.704	3.307
45	0.680	0.850	1.049	1.301	1.679	2.014	2.412	2.690	3.281
50	0.679	0.849	1.047	1.299	1.676	2.009	2.403	2.678	3.261
60	0.679	0.848	1.045	1.296	1.671	2.000	2.390	2.660	3.232
70	0.678	0.847	1.044	1.294	1.667	1.994	2.381	2.648	3.211
80	0.678	0.846	1.043	1.292	1.664	1.990	2.374	2.639	3.195
90	0.677	0.846	1.042	1.291	1.662	1.987	2.368	2.632	3.183
100	0.677	0.845	1.042	1.290	1.660	1.984	2.364	2.626	3.174
120	0.677	0.845	1.041	1.289	1.658	1.980	2.358	2.617	3.160
150	0.676	0.844	1.040	1.287	1.655	1.976	2.351	2.609	3.145
200	0.676	0.843	1.039	1.286	1.653	1.972	2.345	2.601	3.131
500	0.675	0.842	1.038	1.283	1.648	1.965	2.334	2.586	3.107
1000	0.675	0.842	1.037	1.282	1.646	1.962	2.330	2.581	3.098

How to read the table: each cell shows P(T ≤ t) for the selected degrees of freedom. For negative t: P(T ≤ −t) = 1 − P(T ≤ t), or switch the sign with the button.

Degrees of freedom (ν):

Click a cell to read the value.

P(T ≤ t) for t from 0.00 to 6.09

t	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.0	0.5000	0.5039	0.5078	0.5117	0.5156	0.5194	0.5233	0.5272	0.5311	0.5350
0.1	0.5388	0.5427	0.5466	0.5504	0.5543	0.5581	0.5620	0.5658	0.5696	0.5734
0.2	0.5773	0.5811	0.5849	0.5886	0.5924	0.5962	0.5999	0.6037	0.6074	0.6111
0.3	0.6148	0.6185	0.6222	0.6259	0.6296	0.6332	0.6368	0.6405	0.6441	0.6476
0.4	0.6512	0.6548	0.6583	0.6618	0.6654	0.6688	0.6723	0.6758	0.6792	0.6826
0.5	0.6861	0.6894	0.6928	0.6962	0.6995	0.7028	0.7061	0.7094	0.7126	0.7159
0.6	0.7191	0.7223	0.7254	0.7286	0.7317	0.7348	0.7379	0.7410	0.7440	0.7471
0.7	0.7501	0.7530	0.7560	0.7589	0.7618	0.7647	0.7676	0.7704	0.7733	0.7761
0.8	0.7788	0.7816	0.7843	0.7870	0.7897	0.7924	0.7950	0.7977	0.8002	0.8028
0.9	0.8054	0.8079	0.8104	0.8129	0.8153	0.8177	0.8202	0.8225	0.8249	0.8272
1.0	0.8296	0.8318	0.8341	0.8364	0.8386	0.8408	0.8430	0.8451	0.8472	0.8494
1.1	0.8514	0.8535	0.8556	0.8576	0.8596	0.8615	0.8635	0.8654	0.8673	0.8692
1.2	0.8711	0.8729	0.8748	0.8766	0.8784	0.8801	0.8819	0.8836	0.8853	0.8870
1.3	0.8886	0.8903	0.8919	0.8935	0.8951	0.8966	0.8982	0.8997	0.9012	0.9027
1.4	0.9041	0.9056	0.9070	0.9084	0.9098	0.9112	0.9125	0.9138	0.9152	0.9165
1.5	0.9177	0.9190	0.9203	0.9215	0.9227	0.9239	0.9251	0.9263	0.9274	0.9285
1.6	0.9297	0.9308	0.9318	0.9329	0.9340	0.9350	0.9360	0.9371	0.9381	0.9390
1.7	0.9400	0.9410	0.9419	0.9428	0.9438	0.9447	0.9455	0.9464	0.9473	0.9481
1.8	0.9490	0.9498	0.9506	0.9514	0.9522	0.9530	0.9537	0.9545	0.9552	0.9560
1.9	0.9567	0.9574	0.9581	0.9588	0.9595	0.9601	0.9608	0.9614	0.9621	0.9627
2.0	0.9633	0.9639	0.9645	0.9651	0.9657	0.9662	0.9668	0.9674	0.9679	0.9684
2.1	0.9690	0.9695	0.9700	0.9705	0.9710	0.9715	0.9719	0.9724	0.9729	0.9733
2.2	0.9738	0.9742	0.9747	0.9751	0.9755	0.9759	0.9763	0.9767	0.9771	0.9775
2.3	0.9779	0.9782	0.9786	0.9790	0.9793	0.9797	0.9800	0.9804	0.9807	0.9810
2.4	0.9813	0.9817	0.9820	0.9823	0.9826	0.9829	0.9832	0.9834	0.9837	0.9840
2.5	0.9843	0.9845	0.9848	0.9851	0.9853	0.9856	0.9858	0.9861	0.9863	0.9865
2.6	0.9868	0.9870	0.9872	0.9874	0.9876	0.9878	0.9881	0.9883	0.9885	0.9887
2.7	0.9888	0.9890	0.9892	0.9894	0.9896	0.9898	0.9899	0.9901	0.9903	0.9904
2.8	0.9906	0.9908	0.9909	0.9911	0.9912	0.9914	0.9915	0.9917	0.9918	0.9919
2.9	0.9921	0.9922	0.9923	0.9925	0.9926	0.9927	0.9929	0.9930	0.9931	0.9932
3.0	0.9933	0.9934	0.9936	0.9937	0.9938	0.9939	0.9940	0.9941	0.9942	0.9943
3.1	0.9944	0.9945	0.9946	0.9947	0.9947	0.9948	0.9949	0.9950	0.9951	0.9952
3.2	0.9953	0.9953	0.9954	0.9955	0.9956	0.9956	0.9957	0.9958	0.9959	0.9959
3.3	0.9960	0.9961	0.9961	0.9962	0.9963	0.9963	0.9964	0.9964	0.9965	0.9966
3.4	0.9966	0.9967	0.9967	0.9968	0.9968	0.9969	0.9969	0.9970	0.9970	0.9971
3.5	0.9971	0.9972	0.9972	0.9973	0.9973	0.9974	0.9974	0.9975	0.9975	0.9975
3.6	0.9976	0.9976	0.9977	0.9977	0.9977	0.9978	0.9978	0.9978	0.9979	0.9979
3.7	0.9979	0.9980	0.9980	0.9980	0.9981	0.9981	0.9981	0.9982	0.9982	0.9982
3.8	0.9983	0.9983	0.9983	0.9983	0.9984	0.9984	0.9984	0.9984	0.9985	0.9985
3.9	0.9985	0.9985	0.9986	0.9986	0.9986	0.9986	0.9987	0.9987	0.9987	0.9987
4.0	0.9987	0.9988	0.9988	0.9988	0.9988	0.9988	0.9989	0.9989	0.9989	0.9989
4.1	0.9989	0.9989	0.9990	0.9990	0.9990	0.9990	0.9990	0.9990	0.9991	0.9991
4.2	0.9991	0.9991	0.9991	0.9991	0.9991	0.9992	0.9992	0.9992	0.9992	0.9992
4.3	0.9992	0.9992	0.9992	0.9993	0.9993	0.9993	0.9993	0.9993	0.9993	0.9993
4.4	0.9993	0.9993	0.9994	0.9994	0.9994	0.9994	0.9994	0.9994	0.9994	0.9994
4.5	0.9994	0.9994	0.9994	0.9995	0.9995	0.9995	0.9995	0.9995	0.9995	0.9995
4.6	0.9995	0.9995	0.9995	0.9995	0.9995	0.9995	0.9996	0.9996	0.9996	0.9996
4.7	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996
4.8	0.9996	0.9996	0.9996	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997
4.9	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997
5.0	0.9997	0.9997	0.9997	0.9997	0.9997	0.9998	0.9998	0.9998	0.9998	0.9998
5.1	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998
5.2	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998
5.3	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998
5.4	0.9998	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
5.5	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
5.6	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
5.7	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
5.8	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
5.9	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
6.0	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999

P(T ≤ t) for t from −6.09 to −0.00

t	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
−0.0	0.5000	0.4961	0.4922	0.4883	0.4844	0.4806	0.4767	0.4728	0.4689	0.4650
−0.1	0.4612	0.4573	0.4534	0.4496	0.4457	0.4419	0.4380	0.4342	0.4304	0.4266
−0.2	0.4227	0.4189	0.4151	0.4114	0.4076	0.4038	0.4001	0.3963	0.3926	0.3889
−0.3	0.3852	0.3815	0.3778	0.3741	0.3704	0.3668	0.3632	0.3595	0.3559	0.3524
−0.4	0.3488	0.3452	0.3417	0.3382	0.3346	0.3312	0.3277	0.3242	0.3208	0.3174
−0.5	0.3139	0.3106	0.3072	0.3038	0.3005	0.2972	0.2939	0.2906	0.2874	0.2841
−0.6	0.2809	0.2777	0.2746	0.2714	0.2683	0.2652	0.2621	0.2590	0.2560	0.2529
−0.7	0.2499	0.2470	0.2440	0.2411	0.2382	0.2353	0.2324	0.2296	0.2267	0.2239
−0.8	0.2212	0.2184	0.2157	0.2130	0.2103	0.2076	0.2050	0.2023	0.1998	0.1972
−0.9	0.1946	0.1921	0.1896	0.1871	0.1847	0.1823	0.1798	0.1775	0.1751	0.1728
−1.0	0.1704	0.1682	0.1659	0.1636	0.1614	0.1592	0.1570	0.1549	0.1528	0.1506
−1.1	0.1486	0.1465	0.1444	0.1424	0.1404	0.1385	0.1365	0.1346	0.1327	0.1308
−1.2	0.1289	0.1271	0.1252	0.1234	0.1216	0.1199	0.1181	0.1164	0.1147	0.1130
−1.3	0.1114	0.1097	0.1081	0.1065	0.1049	0.1034	0.1018	0.1003	0.0988	0.0973
−1.4	0.0959	0.0944	0.0930	0.0916	0.0902	0.0888	0.0875	0.0862	0.0848	0.0835
−1.5	0.0823	0.0810	0.0797	0.0785	0.0773	0.0761	0.0749	0.0737	0.0726	0.0715
−1.6	0.0703	0.0692	0.0682	0.0671	0.0660	0.0650	0.0640	0.0629	0.0619	0.0610
−1.7	0.0600	0.0590	0.0581	0.0572	0.0562	0.0553	0.0545	0.0536	0.0527	0.0519
−1.8	0.0510	0.0502	0.0494	0.0486	0.0478	0.0470	0.0463	0.0455	0.0448	0.0440
−1.9	0.0433	0.0426	0.0419	0.0412	0.0405	0.0399	0.0392	0.0386	0.0379	0.0373
−2.0	0.0367	0.0361	0.0355	0.0349	0.0343	0.0338	0.0332	0.0326	0.0321	0.0316
−2.1	0.0310	0.0305	0.0300	0.0295	0.0290	0.0285	0.0281	0.0276	0.0271	0.0267
−2.2	0.0262	0.0258	0.0253	0.0249	0.0245	0.0241	0.0237	0.0233	0.0229	0.0225
−2.3	0.0221	0.0218	0.0214	0.0210	0.0207	0.0203	0.0200	0.0196	0.0193	0.0190
−2.4	0.0187	0.0183	0.0180	0.0177	0.0174	0.0171	0.0168	0.0166	0.0163	0.0160
−2.5	0.0157	0.0155	0.0152	0.0149	0.0147	0.0144	0.0142	0.0139	0.0137	0.0135
−2.6	0.0132	0.0130	0.0128	0.0126	0.0124	0.0122	0.0119	0.0117	0.0115	0.0113
−2.7	0.0112	0.0110	0.0108	0.0106	0.0104	0.0102	0.0101	0.0099	0.0097	0.0096
−2.8	0.0094	0.0092	0.0091	0.0089	0.0088	0.0086	0.0085	0.0083	0.0082	0.0081
−2.9	0.0079	0.0078	0.0077	0.0075	0.0074	0.0073	0.0071	0.0070	0.0069	0.0068
−3.0	0.0067	0.0066	0.0064	0.0063	0.0062	0.0061	0.0060	0.0059	0.0058	0.0057
−3.1	0.0056	0.0055	0.0054	0.0053	0.0053	0.0052	0.0051	0.0050	0.0049	0.0048
−3.2	0.0047	0.0047	0.0046	0.0045	0.0044	0.0044	0.0043	0.0042	0.0041	0.0041
−3.3	0.0040	0.0039	0.0039	0.0038	0.0037	0.0037	0.0036	0.0036	0.0035	0.0034
−3.4	0.0034	0.0033	0.0033	0.0032	0.0032	0.0031	0.0031	0.0030	0.0030	0.0029
−3.5	0.0029	0.0028	0.0028	0.0027	0.0027	0.0026	0.0026	0.0025	0.0025	0.0025
−3.6	0.0024	0.0024	0.0023	0.0023	0.0023	0.0022	0.0022	0.0022	0.0021	0.0021
−3.7	0.0021	0.0020	0.0020	0.0020	0.0019	0.0019	0.0019	0.0018	0.0018	0.0018
−3.8	0.0017	0.0017	0.0017	0.0017	0.0016	0.0016	0.0016	0.0016	0.0015	0.0015
−3.9	0.0015	0.0015	0.0014	0.0014	0.0014	0.0014	0.0013	0.0013	0.0013	0.0013
−4.0	0.0013	0.0012	0.0012	0.0012	0.0012	0.0012	0.0011	0.0011	0.0011	0.0011
−4.1	0.0011	0.0011	0.0010	0.0010	0.0010	0.0010	0.0010	0.0010	0.0009	0.0009
−4.2	0.0009	0.0009	0.0009	0.0009	0.0009	0.0008	0.0008	0.0008	0.0008	0.0008
−4.3	0.0008	0.0008	0.0008	0.0007	0.0007	0.0007	0.0007	0.0007	0.0007	0.0007
−4.4	0.0007	0.0007	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006
−4.5	0.0006	0.0006	0.0006	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005
−4.6	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005	0.0004	0.0004	0.0004	0.0004
−4.7	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004
−4.8	0.0004	0.0004	0.0004	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003
−4.9	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003
−5.0	0.0003	0.0003	0.0003	0.0003	0.0003	0.0002	0.0002	0.0002	0.0002	0.0002
−5.1	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
−5.2	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
−5.3	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
−5.4	0.0002	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−5.5	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−5.6	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−5.7	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−5.8	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−5.9	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−6.0	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001

How to read the table: each cell shows the density f(t, ν). The function is symmetric: f(−t, ν) = f(t, ν). As ν increases the curve approaches the standard Normal.

Degrees of freedom (ν):

Click a cell to read the value.

f(t, ν) for t from 0.00 to 6.09 (symmetric: f(−t,ν) = f(t,ν))

t	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.0	0.3891	0.3891	0.3890	0.3889	0.3888	0.3886	0.3883	0.3881	0.3877	0.3874
0.1	0.3870	0.3865	0.3860	0.3855	0.3849	0.3843	0.3837	0.3830	0.3822	0.3815
0.2	0.3807	0.3798	0.3789	0.3780	0.3770	0.3760	0.3750	0.3739	0.3727	0.3716
0.3	0.3704	0.3692	0.3679	0.3666	0.3653	0.3639	0.3625	0.3611	0.3596	0.3581
0.4	0.3566	0.3550	0.3534	0.3518	0.3502	0.3485	0.3468	0.3450	0.3433	0.3415
0.5	0.3397	0.3379	0.3360	0.3341	0.3322	0.3303	0.3283	0.3264	0.3244	0.3224
0.6	0.3203	0.3183	0.3162	0.3141	0.3120	0.3099	0.3078	0.3056	0.3035	0.3013
0.7	0.2991	0.2969	0.2947	0.2925	0.2902	0.2880	0.2857	0.2835	0.2812	0.2789
0.8	0.2766	0.2743	0.2720	0.2697	0.2674	0.2651	0.2628	0.2605	0.2582	0.2559
0.9	0.2535	0.2512	0.2489	0.2466	0.2442	0.2419	0.2396	0.2373	0.2350	0.2327
1.0	0.2304	0.2281	0.2258	0.2235	0.2212	0.2189	0.2166	0.2144	0.2121	0.2099
1.1	0.2076	0.2054	0.2031	0.2009	0.1987	0.1965	0.1943	0.1921	0.1900	0.1878
1.2	0.1857	0.1835	0.1814	0.1793	0.1772	0.1751	0.1730	0.1710	0.1689	0.1669
1.3	0.1649	0.1628	0.1608	0.1589	0.1569	0.1549	0.1530	0.1511	0.1492	0.1473
1.4	0.1454	0.1435	0.1417	0.1398	0.1380	0.1362	0.1344	0.1327	0.1309	0.1292
1.5	0.1274	0.1257	0.1240	0.1224	0.1207	0.1191	0.1174	0.1158	0.1142	0.1126
1.6	0.1111	0.1095	0.1080	0.1065	0.1050	0.1035	0.1020	0.1006	0.0991	0.0977
1.7	0.0963	0.0949	0.0935	0.0922	0.0908	0.0895	0.0882	0.0869	0.0856	0.0844
1.8	0.0831	0.0819	0.0807	0.0795	0.0783	0.0771	0.0759	0.0748	0.0736	0.0725
1.9	0.0714	0.0703	0.0693	0.0682	0.0671	0.0661	0.0651	0.0641	0.0631	0.0621
2.0	0.0611	0.0602	0.0592	0.0583	0.0574	0.0565	0.0556	0.0547	0.0539	0.0530
2.1	0.0522	0.0513	0.0505	0.0497	0.0489	0.0481	0.0474	0.0466	0.0458	0.0451
2.2	0.0444	0.0437	0.0430	0.0423	0.0416	0.0409	0.0402	0.0396	0.0389	0.0383
2.3	0.0377	0.0370	0.0364	0.0358	0.0352	0.0347	0.0341	0.0335	0.0330	0.0324
2.4	0.0319	0.0313	0.0308	0.0303	0.0298	0.0293	0.0288	0.0283	0.0279	0.0274
2.5	0.0269	0.0265	0.0260	0.0256	0.0252	0.0247	0.0243	0.0239	0.0235	0.0231
2.6	0.0227	0.0223	0.0220	0.0216	0.0212	0.0209	0.0205	0.0202	0.0198	0.0195
2.7	0.0192	0.0188	0.0185	0.0182	0.0179	0.0176	0.0173	0.0170	0.0167	0.0164
2.8	0.0161	0.0158	0.0156	0.0153	0.0150	0.0148	0.0145	0.0143	0.0140	0.0138
2.9	0.0136	0.0133	0.0131	0.0129	0.0127	0.0124	0.0122	0.0120	0.0118	0.0116
3.0	0.0114	0.0112	0.0110	0.0108	0.0106	0.0105	0.0103	0.0101	0.0099	0.0097
3.1	0.0096	0.0094	0.0093	0.0091	0.0089	0.0088	0.0086	0.0085	0.0083	0.0082
3.2	0.0081	0.0079	0.0078	0.0076	0.0075	0.0074	0.0073	0.0071	0.0070	0.0069
3.3	0.0068	0.0067	0.0065	0.0064	0.0063	0.0062	0.0061	0.0060	0.0059	0.0058
3.4	0.0057	0.0056	0.0055	0.0054	0.0053	0.0052	0.0051	0.0050	0.0050	0.0049
3.5	0.0048	0.0047	0.0046	0.0045	0.0045	0.0044	0.0043	0.0042	0.0042	0.0041
3.6	0.0040	0.0040	0.0039	0.0038	0.0038	0.0037	0.0036	0.0036	0.0035	0.0034
3.7	0.0034	0.0033	0.0033	0.0032	0.0032	0.0031	0.0031	0.0030	0.0030	0.0029
3.8	0.0029	0.0028	0.0028	0.0027	0.0027	0.0026	0.0026	0.0025	0.0025	0.0024
3.9	0.0024	0.0024	0.0023	0.0023	0.0022	0.0022	0.0022	0.0021	0.0021	0.0021
4.0	0.0020	0.0020	0.0020	0.0019	0.0019	0.0019	0.0018	0.0018	0.0018	0.0017
4.1	0.0017	0.0017	0.0017	0.0016	0.0016	0.0016	0.0016	0.0015	0.0015	0.0015
4.2	0.0015	0.0014	0.0014	0.0014	0.0014	0.0013	0.0013	0.0013	0.0013	0.0012
4.3	0.0012	0.0012	0.0012	0.0012	0.0011	0.0011	0.0011	0.0011	0.0011	0.0011
4.4	0.0010	0.0010	0.0010	0.0010	0.0010	0.0010	0.0009	0.0009	0.0009	0.0009
4.5	0.0009	0.0009	0.0009	0.0008	0.0008	0.0008	0.0008	0.0008	0.0008	0.0008
4.6	0.0008	0.0007	0.0007	0.0007	0.0007	0.0007	0.0007	0.0007	0.0007	0.0006
4.7	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006	0.0006
4.8	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005
4.9	0.0005	0.0005	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004
5.0	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0003	0.0003
5.1	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003
5.2	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003
5.3	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
5.4	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
5.5	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
5.6	0.0002	0.0002	0.0002	0.0002	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
5.7	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
5.8	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
5.9	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
6.0	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001

How to use these tables

Student's t Distribution

Student's t distribution with ν degrees of freedom has density function:

\( f(t,\nu) = \dfrac{\Gamma\!\left(\tfrac{\nu+1}{2}\right)}{\sqrt{\nu\pi}\;\Gamma\!\left(\tfrac{\nu}{2}\right)} \left(1+\dfrac{t^2}{\nu}\right)^{-\frac{\nu+1}{2}} \)

As ν → ∞ the distribution converges to the standard Normal N(0,1).

Critical values table

Shows the quantiles t_α,ν such that P(T > t_α,ν) = α (one-tailed test). For a two-tailed test at level α₂, use column α₁ = α₂/2.

Example: two-tailed test α = 0.05, ν = 20 → column α₁ = 0.025 → t = 2.086.
When ν = ∞ the values match the quantiles of the standard Normal.

Cumulative distribution table

Each cell shows P(T ≤ t) for the selected number of degrees of freedom. To compute two-tailed p-values: p = 2 · P(T > |t_obs|) = 2 · (1 − P(T ≤ |t_obs|)).

Student's t Table (Critical Values)

How to use these tables

Student's t Distribution

Critical values table

Cumulative distribution table

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