Statistics - T-table
The Student's t-distribution is similar to a normal distribution. But it is adjusted for uncertainty with smaller sample sizes.
Smaller sample sizes give fewer degrees of freedom (df), which makes the tails larger.
T-Distribution and Table of Critical T-Values
The numbers in the table cells correspond to critical t-values for different tail-areas (α).
The tail areas are probabilities. For example, 0.05 is 5% percent probability.
Each row corresponds to different degrees of freedom (df).
| One tail | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 |
|---|---|---|---|---|---|---|---|
| Two tails | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
| df | |||||||
| 1 | 6.3138 | 12.7062 | 31.8205 | 63.6567 | 127.3213 | 318.3088 | 636.6192 |
| 2 | 2.9200 | 4.3027 | 6.9646 | 9.9248 | 14.0890 | 22.3271 | 31.5991 |
| 3 | 2.3534 | 3.1824 | 4.5407 | 5.8409 | 7.4533 | 10.2145 | 12.9240 |
| 4 | 2.1318 | 2.7764 | 3.7469 | 4.6041 | 5.5976 | 7.1732 | 8.6103 |
| 5 | 2.0150 | 2.5706 | 3.3649 | 4.0321 | 4.7733 | 5.8934 | 6.8688 |
| 6 | 1.9432 | 2.4469 | 3.1427 | 3.7074 | 4.3168 | 5.2076 | 5.9588 |
| 7 | 1.8946 | 2.3646 | 2.9980 | 3.4995 | 4.0293 | 4.7853 | 5.4079 |
| 8 | 1.8595 | 2.3060 | 2.8965 | 3.3554 | 3.8325 | 4.5008 | 5.0413 |
| 9 | 1.8331 | 2.2622 | 2.8214 | 3.2498 | 3.6897 | 4.2968 | 4.7809 |
| 10 | 1.8125 | 2.2281 | 2.7638 | 3.1693 | 3.5814 | 4.1437 | 4.5869 |
| 11 | 1.7959 | 2.2010 | 2.7181 | 3.1058 | 3.4966 | 4.0247 | 4.4370 |
| 12 | 1.7823 | 2.1788 | 2.6810 | 3.0545 | 3.4284 | 3.9296 | 4.3178 |
| 13 | 1.7709 | 2.1604 | 2.6503 | 3.0123 | 3.3725 | 3.8520 | 4.2208 |
| 14 | 1.7613 | 2.1448 | 2.6245 | 2.9768 | 3.3257 | 3.7874 | 4.1405 |
| 15 | 1.7531 | 2.1314 | 2.6025 | 2.9467 | 3.2860 | 3.7328 | 4.0728 |
| 16 | 1.7459 | 2.1199 | 2.5835 | 2.9208 | 3.2520 | 3.6862 | 4.0150 |
| 17 | 1.7396 | 2.1098 | 2.5669 | 2.8982 | 3.2224 | 3.6458 | 3.9651 |
| 18 | 1.7341 | 2.1009 | 2.5524 | 2.8784 | 3.1966 | 3.6105 | 3.9216 |
| 19 | 1.7291 | 2.0930 | 2.5395 | 2.8609 | 3.1737 | 3.5794 | 3.8834 |
| 20 | 1.7247 | 2.0860 | 2.5280 | 2.8453 | 3.1534 | 3.5518 | 3.8495 |
| 21 | 1.7207 | 2.0796 | 2.5176 | 2.8314 | 3.1352 | 3.5272 | 3.8193 |
| 22 | 1.7171 | 2.0739 | 2.5083 | 2.8188 | 3.1188 | 3.5050 | 3.7921 |
| 23 | 1.7139 | 2.0687 | 2.4999 | 2.8073 | 3.1040 | 3.4850 | 3.7676 |
| 24 | 1.7109 | 2.0639 | 2.4922 | 2.7969 | 3.0905 | 3.4668 | 3.7454 |
| 25 | 1.7081 | 2.0595 | 2.4851 | 2.7874 | 3.0782 | 3.4502 | 3.7251 |
| 26 | 1.7056 | 2.0555 | 2.4786 | 2.7787 | 3.0669 | 3.4350 | 3.7066 |
| 27 | 1.7033 | 2.0518 | 2.4727 | 2.7707 | 3.0565 | 3.4210 | 3.6896 |
| 28 | 1.7011 | 2.0484 | 2.4671 | 2.7633 | 3.0469 | 3.4082 | 3.6739 |
| 29 | 1.6991 | 2.0452 | 2.4620 | 2.7564 | 3.0380 | 3.3962 | 3.6594 |
| 30 | 1.6973 | 2.0423 | 2.4573 | 2.7500 | 3.0298 | 3.3852 | 3.6460 |
| 31 | 1.6955 | 2.0395 | 2.4528 | 2.7440 | 3.0221 | 3.3749 | 3.6335 |
| 32 | 1.6939 | 2.0369 | 2.4487 | 2.7385 | 3.0149 | 3.3653 | 3.6218 |
| 33 | 1.6924 | 2.0345 | 2.4448 | 2.7333 | 3.0082 | 3.3563 | 3.6109 |
| 34 | 1.6909 | 2.0322 | 2.4411 | 2.7284 | 3.0020 | 3.3479 | 3.6007 |
| 35 | 1.6896 | 2.0301 | 2.4377 | 2.7238 | 2.9960 | 3.3400 | 3.5911 |
| 36 | 1.6883 | 2.0281 | 2.4345 | 2.7195 | 2.9905 | 3.3326 | 3.5821 |
| 37 | 1.6871 | 2.0262 | 2.4314 | 2.7154 | 2.9852 | 3.3256 | 3.5737 |
| 38 | 1.6860 | 2.0244 | 2.4286 | 2.7116 | 2.9803 | 3.3190 | 3.5657 |
| 39 | 1.6849 | 2.0227 | 2.4258 | 2.7079 | 2.9756 | 3.3128 | 3.5581 |
| 40 | 1.6839 | 2.0211 | 2.4233 | 2.7045 | 2.9712 | 3.3069 | 3.5510 |
| 41 | 1.6829 | 2.0195 | 2.4208 | 2.7012 | 2.9670 | 3.3013 | 3.5442 |
| 42 | 1.6820 | 2.0181 | 2.4185 | 2.6981 | 2.9630 | 3.2960 | 3.5377 |
| 43 | 1.6811 | 2.0167 | 2.4163 | 2.6951 | 2.9592 | 3.2909 | 3.5316 |
| 44 | 1.6802 | 2.0154 | 2.4141 | 2.6923 | 2.9555 | 3.2861 | 3.5258 |
| 45 | 1.6794 | 2.0141 | 2.4121 | 2.6896 | 2.9521 | 3.2815 | 3.5203 |
| 46 | 1.6787 | 2.0129 | 2.4102 | 2.6870 | 2.9488 | 3.2771 | 3.5150 |
| 47 | 1.6779 | 2.0117 | 2.4083 | 2.6846 | 2.9456 | 3.2729 | 3.5099 |
| 48 | 1.6772 | 2.0106 | 2.4066 | 2.6822 | 2.9426 | 3.2689 | 3.5051 |
| 49 | 1.6766 | 2.0096 | 2.4049 | 2.6800 | 2.9397 | 3.2651 | 3.5004 |
| 50 | 1.6759 | 2.0086 | 2.4033 | 2.6778 | 2.9370 | 3.2614 | 3.4960 |
| 60 | 1.6706 | 2.0003 | 2.3901 | 2.6603 | 2.9146 | 3.2317 | 3.4602 |
| 70 | 1.6669 | 1.9944 | 2.3808 | 2.6479 | 2.8987 | 3.2108 | 3.4350 |
| 80 | 1.6641 | 1.9901 | 2.3739 | 2.6387 | 2.8870 | 3.1953 | 3.4163 |
| 90 | 1.6620 | 1.9867 | 2.3685 | 2.6316 | 2.8779 | 3.1833 | 3.4019 |
| 100 | 1.6602 | 1.9840 | 2.3642 | 2.6259 | 2.8707 | 3.1737 | 3.3905 |
| 200 | 1.6525 | 1.9719 | 2.3451 | 2.6006 | 2.8385 | 3.1315 | 3.3398 |
| 300 | 1.6499 | 1.9679 | 2.3388 | 2.5923 | 2.8279 | 3.1176 | 3.3233 |
| 400 | 1.6487 | 1.9659 | 2.3357 | 2.5882 | 2.8227 | 3.1107 | 3.3150 |
| 500 | 1.6479 | 1.9647 | 2.3338 | 2.5857 | 2.8195 | 3.1066 | 3.3101 |
| 600 | 1.6474 | 1.9639 | 2.3326 | 2.5840 | 2.8175 | 3.1039 | 3.3068 |
| 700 | 1.6470 | 1.9634 | 2.3317 | 2.5829 | 2.8160 | 3.1019 | 3.3045 |
| 800 | 1.6468 | 1.9629 | 2.3310 | 2.5820 | 2.8148 | 3.1005 | 3.3027 |
| 900 | 1.6465 | 1.9626 | 2.3305 | 2.5813 | 2.8140 | 3.0993 | 3.3014 |
| 1000 | 1.6464 | 1.9623 | 2.3301 | 2.5808 | 2.8133 | 3.0984 | 3.3003 |
| 10000 | 1.6450 | 1.9602 | 2.3267 | 2.5763 | 2.8077 | 3.0910 | 3.2915 |
| ∞ | 1.6449 | 1.9600 | 2.3263 | 2.5758 | 2.8070 | 3.0902 | 3.2905 |
