T-Table

Student's t critical values and p-values by degrees of freedom, with reverse lookup.

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Full printable reference table
Student's t critical values
dfα = 0.1α = 0.05α = 0.025α = 0.01α = 0.005α = 0.001
16.31412.70625.45263.657127.321636.619
22.9204.3036.2059.92514.08931.599
32.3533.1824.1775.8417.45312.924
42.1322.7763.4954.6045.5988.610
52.0152.5713.1634.0324.7736.869
61.9432.4472.9693.7074.3175.959
71.8952.3652.8413.4994.0295.408
81.8602.3062.7523.3553.8335.041
91.8332.2622.6853.2503.6904.781
101.8122.2282.6343.1693.5814.587
111.7962.2012.5933.1063.4974.437
121.7822.1792.5603.0553.4284.318
131.7712.1602.5333.0123.3724.221
141.7612.1452.5102.9773.3264.140
151.7532.1312.4902.9473.2864.073
161.7462.1202.4732.9213.2524.015
171.7402.1102.4582.8983.2223.965
181.7342.1012.4452.8783.1973.922
191.7292.0932.4332.8613.1743.883
201.7252.0862.4232.8453.1533.850
211.7212.0802.4142.8313.1353.819
221.7172.0742.4052.8193.1193.792
231.7142.0692.3982.8073.1043.768
241.7112.0642.3912.7973.0913.745
251.7082.0602.3852.7873.0783.725
261.7062.0562.3792.7793.0673.707
271.7032.0522.3732.7713.0573.690
281.7012.0482.3682.7633.0473.674
291.6992.0452.3642.7563.0383.659
301.6972.0422.3602.7503.0303.646
401.6842.0212.3292.7042.9713.551
601.6712.0002.2992.6602.9153.460
801.6641.9902.2842.6392.8873.416
1001.6601.9842.2762.6262.8713.390
1201.6581.9802.2702.6172.8603.373

About this tool

Enter degrees of freedom, alpha and tail to get the t critical value, or switch to p-value mode and enter a t statistic. It replaces the printed table with an exact calculation for any df.

How to use

1
Step 1
Choose critical value or p-value mode.
2
Step 2
Enter degrees of freedom and alpha (or the t statistic).
3
Step 3
Pick the tail and press Calculate.

How it works

A t critical value marks the point beyond which the sample t statistic is significant at your alpha. Two-tailed tests split alpha across both tails, so the cut-off is larger than for a one-tailed test at the same alpha. As df grows, t approaches the normal value 1.96.

Reject H₀ when |t| > t(α/2, df) (two-tailed)      p = 2 × P(T > |t|)

Worked example

df = 24, α = 0.05, two-tailed

Input
Critical value, df = 24, α = 0.05, two-tailed
Output
2.0639
Walkthrough
The cut-off leaves 2.5% in each tail. Reversing it: t = 2.064 with df 24, two-tailed, gives p = 0.04999.

Limitations

  • Exact values to six decimals; textbooks round to three.
  • Left and right tails are mirror images for t.

Questions

What is the t critical value for df = 24 at 0.05?
2.0639 two-tailed.
What is the one-tailed t critical value for df = 10 at 0.05?
1.8125.
What df should I use for a one-sample t-test?
n − 1, where n is the sample size.

Features

  • Critical value and p-value
  • Any df
  • Runs in your browser

Guides

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

  • Finding mean, median, and mode

    Khan Academy

    Baseline summary stats for coursework checkoffs.

    Watch on YouTube

  • Student's t-distribution

    Khan Academy

    Why t-tables differ from z for small samples.

    Watch on YouTube

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