t-distribution Table

T-Distribution Table

Student’s T-Distribution Table

This table shows critical values of the t-distribution for both one-tailed and two-tailed tests.

df α = 0.1α = 0.05α = 0.01
One-TailTwo-TailOne-TailTwo-TailOne-TailTwo-Tail
13.07776.31386.313812.706231.820563.6567
21.88562.92002.92004.30276.96469.9248
31.63772.35342.35343.18244.54075.8409
41.53322.13182.13182.77643.74694.6041
51.47592.01502.01502.57063.36494.0321
61.43981.94321.94322.44693.14273.7074
71.41491.89461.89462.36462.99803.4995
81.39681.85951.85952.30602.89653.3554
91.38301.83311.83312.26222.82143.2498
101.37221.81251.81252.22812.76383.1693
111.36341.79591.79592.20102.71813.1058
121.35621.78231.78232.17882.68103.0545
131.35021.77091.77092.16042.65033.0123
141.34501.76131.76132.14482.62452.9768
151.34061.75311.75312.13142.60252.9467
161.33681.74591.74592.11992.58352.9208
171.33341.73961.73962.10982.56692.8982
181.33041.73411.73412.10092.55242.8784
191.32771.72911.72912.09302.53952.8609
201.32531.72471.72472.08602.52802.8453
211.32321.72071.72072.07962.51762.8314
221.32121.71711.71712.07392.50832.8188
231.31951.71391.71392.06872.49992.8073
241.31781.71091.71092.06392.49222.7969
251.31631.70811.70812.05952.48512.7874
261.31501.70561.70562.05552.47862.7787
271.31371.70331.70332.05182.47272.7707
281.31251.70111.70112.04842.46712.7633
291.31141.69911.69912.04522.46202.7564
301.31041.69731.69732.04232.45732.7500
401.30311.68391.68392.02112.42332.7045
501.29871.67591.67592.00862.40332.6778
601.29581.67061.67062.00032.39012.6603
701.29381.66691.66691.99442.38082.6479
801.29221.66411.66411.99012.37392.6387
901.29101.66201.66201.98672.36852.6316
1001.29011.66021.66021.98402.36422.6259
2001.28581.65251.65251.97192.34512.6006
5001.28321.64791.64791.96472.33382.5857
10001.28241.64641.64641.96232.33012.5808
  1. How to find the critical t-value?
    For instance, you know the df=10 (left-most column) and alpha = 0.05 (two-tail), you can then find the critical value of 2.2281.
  2. What does two-tail mean in t-distribution?
    Two-tailed means we’re interested in results that could be significantly different in either direction – either unusually high OR unusually low. We split our alpha (significance level) between both tails. You can see the visual example below, where df=10, alpha = 0.05 (two-tail). We can see the critical value of 2.228.
  3. What does one-tail mean in t-distribution?
    In one-tailed tests, we put all of alpha (significance level) in one tail We’re testing if something is either: Significantly GREATER than (right-tailed test) vs. Significantly LESS than (left-tailed test). The following figure is for a right-tailed test. It has df=10, alpha = 0.05 (one-tail), and the critical value of 1.812.

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