Statistics Reference

T-Table for α = 0.05 (t Critical Values)

The workhorse t-table column: critical values at the conventional 5% level for every degree of freedom from 1 to 100 (plus the large-sample tail). The two-tail column is the one behind 95% confidence intervals and standard two-sided t-tests; the one-tail column serves directional tests.

How to Read This Table

Rows are degrees of freedom — every integer from 1 to 100, then 120, 150, 200, 500, and 1000, finer than the stepped rows of the main table. The one-tail column puts all of α = 0.05 in a single tail (directional tests); the two-tail column splits it across both tails (non-directional tests and confidence intervals). The distribution is symmetric, so lower-tail tests use the negative of the printed value.

Two-sided one-sample t-test, n = 11 (df = 10), α = 0.05:

  1. Row df = 10, two-tail column: 2.228 — reject when |t| exceeds it.
  2. A directional version of the same test reads the one-tail column: 1.812.
  3. A 95% CI from the same sample uses the two-tail 2.228 as its multiplier.

Common uses of this level:

  • 95% confidence intervals for a mean (two-tail column)
  • Standard two-sided t-tests at α = 0.05
  • Directional (one-sided) t-tests at 5% (one-tail column)

t Critical Values, α = 0.05, df 1–1000

Student's t critical values at significance level 0.05 for degrees of freedom 1 to 1000
dfOne-tail α = 0.05Two-tail α = 0.05
16.31412.706
22.9204.303
32.3533.182
42.1322.776
52.0152.571
61.9432.447
71.8952.365
81.8602.306
91.8332.262
101.8122.228
111.7962.201
121.7822.179
131.7712.160
141.7612.145
151.7532.131
161.7462.120
171.7402.110
181.7342.101
191.7292.093
201.7252.086
211.7212.080
221.7172.074
231.7142.069
241.7112.064
251.7082.060
261.7062.056
271.7032.052
281.7012.048
291.6992.045
301.6972.042
311.6962.040
321.6942.037
331.6922.035
341.6912.032
351.6902.030
361.6882.028
371.6872.026
381.6862.024
391.6852.023
401.6842.021
411.6832.020
421.6822.018
431.6812.017
441.6802.015
451.6792.014
461.6792.013
471.6782.012
481.6772.011
491.6772.010
501.6762.009
511.6752.008
521.6752.007
531.6742.006
541.6742.005
551.6732.004
561.6732.003
571.6722.002
581.6722.002
591.6712.001
601.6712.000
611.6702.000
621.6701.999
631.6691.998
641.6691.998
651.6691.997
661.6681.997
671.6681.996
681.6681.995
691.6671.995
701.6671.994
711.6671.994
721.6661.993
731.6661.993
741.6661.993
751.6651.992
761.6651.992
771.6651.991
781.6651.991
791.6641.990
801.6641.990
811.6641.990
821.6641.989
831.6631.989
841.6631.989
851.6631.988
861.6631.988
871.6631.988
881.6621.987
891.6621.987
901.6621.987
911.6621.986
921.6621.986
931.6611.986
941.6611.986
951.6611.985
961.6611.985
971.6611.985
981.6611.984
991.6601.984
1001.6601.984
1201.6581.980
1501.6551.976
2001.6531.972
5001.6481.965
10001.6461.962

Other Significance Levels

The t-table overview carries the classic multi-column grid, degrees-of-freedom rules, and the z-convergence walkthrough. The other levels each have a dedicated page:

Frequently Asked Questions

Is this the t value used for a 95% confidence interval?

Yes - the two-tail column at your degrees of freedom is the multiplier: mean ± t × standard error. At df = 10 that is 2.228, falling toward 1.984 at df = 100 and 1.962 at df = 1000, approaching the z value 1.96 from above.

Why are there two different '5%' critical values?

Direction. One-tailed tests place the whole 5% in a single tail (1.812 at df = 10); two-tailed tests split it into 2.5% per side (2.228). The same column bookkeeping appears on every t-table - this page simply prints both readings side by side so no header gymnastics are needed.

What degrees of freedom do I use?

n - 1 for one-sample and paired tests, n1 + n2 - 2 for the classic pooled two-sample test, n - 2 for a simple regression slope. With df beyond 100, use the 120-1000 rows or the z approximation - by then the values differ only in the third decimal.

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