Critical Values of the t-Distribution
Percent |
75 |
90 |
95 |
97.5 |
99 |
99.5 |
99.75 |
99.9 |
99.95 |
99.975 |
99.99 |
99.995
|
One-sided α |
0.25 |
0.1 |
0.05 |
0.025 |
0.01 |
0.005 |
0.0025 |
0.001 |
0.0005 |
0.00025 |
0.0001 |
0.00005
|
Two-sided α |
0.5 |
0.2 |
0.1 |
0.05 |
0.02 |
0.01 |
0.005 |
0.002 |
0.001 |
0.0005 |
0.0002 |
0.0001
|
Degrees of Freedom |
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1 |
3.08 |
6.31 |
12.71 |
31.82 |
63.66 |
127.32 |
318.31 |
636.62 |
1273.24 |
3183.1 |
6366.2 |
2 |
0.82 |
1.89 |
2.92 |
4.3 |
6.96 |
9.22 |
14.09 |
22.33 |
31.6 |
44.7 |
70.7 |
99.99 |
3 |
0.76 |
1.64 |
2.35 |
3.18 |
4.54 |
5.84 |
7.45 |
10.21 |
12.92 |
16.33 |
22.2 |
28 |
4 |
0.74 |
1.53 |
2.13 |
2.78 |
3.75 |
4.6 |
5.6 |
7.17 |
8.61 |
10.31 |
13.03 |
15.54 |
5 |
0.73 |
1.48 |
2.02 |
2.57 |
3.37 |
4.03 |
4.77 |
5.89 |
6.87 |
7.98 |
9.68 |
11.18 |
6 |
0.72 |
1.44 |
1.94 |
2.45 |
3.14 |
3.71 |
4.32 |
5.21 |
5.96 |
6.79 |
8.02 |
9.08 |
7 |
0.71 |
1.42 |
1.9 |
2.37 |
3 |
3.5 |
4.03 |
4.79 |
5.41 |
6.08 |
7.06 |
7.88 |
8 |
0.71 |
1.4 |
1.86 |
2.31 |
2.9 |
3.36 |
3.83 |
4.5 |
5.04 |
5.62 |
6.44 |
7.12 |
9 |
0.7 |
1.38 |
1.83 |
2.26 |
2.82 |
3.25 |
3.69 |
4.3 |
4.78 |
5.29 |
6.01 |
6.59 |
10 |
0.7 |
1.37 |
1.81 |
2.23 |
2.76 |
3.17 |
3.58 |
4.14 |
4.59 |
5.05 |
5.69 |
6.21 |
11 |
0.7 |
1.36 |
1.8 |
2.2 |
2.72 |
3.11 |
3.5 |
4.03 |
4.44 |
4.86 |
5.45 |
5.92 |
12 |
0.7 |
1.36 |
1.78 |
2.18 |
2.68 |
3.06 |
3.43 |
3.93 |
4.32 |
4.72 |
5.26 |
5.69 |
13 |
0.69 |
1.35 |
1.77 |
2.16 |
2.65 |
3.01 |
3.37 |
3.85 |
4.22 |
4.6 |
5.11 |
5.51 |
14 |
0.69 |
1.35 |
1.76 |
2.15 |
2.63 |
2.98 |
3.33 |
3.79 |
4.14 |
4.5 |
4.99 |
5.36 |
15 |
0.69 |
1.34 |
1.75 |
2.13 |
2.6 |
2.95 |
3.29 |
3.73 |
4.07 |
4.42 |
4.88 |
5.24 |
16 |
0.69 |
1.34 |
1.75 |
2.12 |
2.58 |
2.92 |
3.25 |
3.69 |
4.02 |
4.35 |
4.79 |
5.13 |
17 |
0.69 |
1.33 |
1.74 |
2.11 |
2.57 |
2.9 |
3.22 |
3.65 |
3.97 |
4.29 |
4.71 |
5.04 |
18 |
0.69 |
1.33 |
1.73 |
2.1 |
2.55 |
2.88 |
3.2 |
3.61 |
3.92 |
4.23 |
4.65 |
4.97 |
19 |
0.69 |
1.33 |
1.73 |
2.09 |
2.54 |
2.86 |
3.17 |
3.58 |
3.88 |
4.19 |
4.59 |
4.9 |
20 |
0.69 |
1.33 |
1.73 |
2.09 |
2.53 |
2.85 |
3.15 |
3.55 |
3.85 |
4.15 |
4.54 |
4.84 |
21 |
0.69 |
1.32 |
1.72 |
2.08 |
2.52 |
2.83 |
3.14 |
3.53 |
3.82 |
4.11 |
4.49 |
4.78 |
22 |
0.69 |
1.32 |
1.72 |
2.07 |
2.51 |
2.82 |
3.12 |
3.51 |
3.79 |
4.08 |
4.45 |
4.74 |
23 |
0.68 |
1.32 |
1.71 |
2.07 |
2.5 |
2.81 |
3.1 |
3.49 |
3.77 |
4.05 |
4.42 |
4.69 |
24 |
0.68 |
1.32 |
1.71 |
2.06 |
2.49 |
2.8 |
3.09 |
3.47 |
3.75 |
4.02 |
4.38 |
4.65 |
25 |
0.68 |
1.32 |
1.71 |
2.06 |
2.49 |
2.79 |
3.08 |
3.45 |
3.73 |
4 |
4.35 |
4.62 |
26 |
0.68 |
1.32 |
1.71 |
2.06 |
2.48 |
2.78 |
3.07 |
3.44 |
3.71 |
3.97 |
4.32 |
4.59 |
27 |
0.68 |
1.31 |
1.7 |
2.05 |
2.47 |
2.77 |
3.06 |
3.42 |
3.69 |
3.95 |
4.3 |
4.56 |
28 |
0.68 |
1.31 |
1.7 |
2.05 |
2.47 |
2.76 |
3.05 |
3.41 |
3.67 |
3.94 |
4.28 |
4.53 |
29 |
0.68 |
1.31 |
1.7 |
2.05 |
2.46 |
2.76 |
3.04 |
3.4 |
3.66 |
3.92 |
4.25 |
4.51 |
30 |
0.68 |
1.31 |
1.7 |
2.04 |
2.46 |
2.75 |
3.03 |
3.39 |
3.65 |
3.9 |
4.23 |
4.48 |
35 |
0.68 |
1.31 |
1.69 |
2.03 |
2.44 |
2.72 |
3 |
3.34 |
3.59 |
3.84 |
4.15 |
4.39 |
40 |
0.68 |
1.3 |
1.68 |
2.02 |
2.42 |
2.7 |
2.97 |
3.31 |
3.55 |
3.79 |
4.09 |
4.32 |
45 |
0.68 |
1.3 |
1.68 |
2.01 |
2.41 |
2.69 |
2.95 |
3.28 |
3.52 |
3.75 |
4.05 |
4.27 |
50 |
0.68 |
1.3 |
1.68 |
2.01 |
2.4 |
2.68 |
2.94 |
3.26 |
3.5 |
3.72 |
4.01 |
4.23 |
55 |
0.68 |
1.3 |
1.67 |
2 |
2.4 |
2.67 |
2.93 |
3.25 |
3.48 |
3.7 |
3.99 |
4.2 |
60 |
0.68 |
1.3 |
1.67 |
2 |
2.39 |
2.66 |
2.91 |
3.23 |
3.46 |
3.68 |
3.96 |
4.17 |
65 |
0.68 |
1.29 |
1.67 |
2 |
2.39 |
2.65 |
2.91 |
3.22 |
3.45 |
3.66 |
3.94 |
4.15 |
70 |
0.68 |
1.29 |
1.67 |
1.99 |
2.38 |
2.65 |
2.9 |
3.21 |
3.44 |
3.65 |
3.93 |
4.13 |
75 |
0.68 |
1.29 |
1.67 |
1.99 |
2.38 |
2.64 |
2.89 |
3.2 |
3.43 |
3.64 |
3.91 |
4.11 |
80 |
0.68 |
1.29 |
1.66 |
1.99 |
2.37 |
2.64 |
2.89 |
3.2 |
3.42 |
3.63 |
3.9 |
4.1 |
85 |
0.68 |
1.29 |
1.66 |
1.99 |
2.37 |
2.64 |
2.88 |
3.19 |
3.41 |
3.62 |
3.89 |
4.08 |
90 |
0.68 |
1.29 |
1.66 |
1.99 |
2.37 |
2.63 |
2.88 |
3.18 |
3.4 |
3.61 |
3.88 |
4.07 |
95 |
0.68 |
1.29 |
1.66 |
1.99 |
2.37 |
2.63 |
2.87 |
3.18 |
3.4 |
3.6 |
3.87 |
4.06 |
100 |
0.68 |
1.29 |
1.66 |
1.98 |
2.36 |
2.63 |
2.87 |
3.17 |
3.39 |
3.6 |
3.86 |
4.05 |
200 |
0.68 |
1.29 |
1.65 |
1.97 |
2.35 |
2.6 |
2.84 |
3.13 |
3.34 |
3.54 |
3.79 |
3.97 |
500 |
0.68 |
1.28 |
1.65 |
1.97 |
2.33 |
2.59 |
2.82 |
3.11 |
3.31 |
3.5 |
3.75 |
3.92 |
∞ |
0.67 |
1.28 |
1.65 |
1.96 |
2.33 |
2.58 |
2.81 |
3.1 |
3.3 |
3.49 |
3.73 |
3.91 |