T Table Calculator

A t table gives the critical value from the Student’s t distribution for a chosen confidence level, degrees of freedom, and number of tails. That critical value is the cutoff your t statistic must beat to be significant. This t table calculator replaces flipping through a printed table — enter the degrees of freedom, pick a confidence level and tail count, and it returns the exact critical t value.

How to use this calculator

1. Enter the degrees of freedom — for a one-sample test this is the sample size minus one (n − 1).
2. Pick a confidence level (90%, 95%, or 99%).
3. Choose one-tailed or two-tailed, depending on whether your test looks for a difference in one direction or either direction.
4. Read the critical t value. Compare your test’s t statistic against it: if your value is larger in magnitude, the result is significant at that level.

Fewer degrees of freedom push the critical value higher, because small samples carry more uncertainty.

Worked example

Suppose you ran a test with 10 degrees of freedom and want the two-tailed critical value at 95% confidence. A two-tailed 95% level splits the remaining 5% into two tails of 2.5% each:

confidence level = 0.95
alpha = 1 − 0.95 = 0.05
tail area each side = 0.025
degrees of freedom = 10
critical t ≈ 2.228

So any t statistic above 2.228 or below −2.228 is significant at the 5% level with 10 degrees of freedom. For the full reference grid of these cutoffs, see the NIST/SEMATECH e-Handbook table of critical values of the Student’s t distribution.

Frequently asked questions

What are degrees of freedom in a t distribution table?

Degrees of freedom reflect how much independent information your sample carries. For a one-sample t-test it equals n − 1. As degrees of freedom rise, the t distribution narrows toward the standard normal, so the critical t value shrinks.

What is the difference between a one-tailed and two-tailed critical t value?

A one-tailed value puts the whole alpha in a single tail, so it is smaller and easier to exceed. A two-tailed value splits alpha across both tails, raising the cutoff because you are testing for a difference in either direction.

Why does my critical t value differ slightly from a printed table?

Printed tables round to two or three decimals and list only common degrees of freedom. This calculator computes the exact value, so it may differ in the last digit from a rounded textbook entry.