T Distribution Calculator (p & Critical t)

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T Distribution Calculator

This t distribution calculator does two jobs. In probability mode it converts a t statistic and its degrees of freedom into a left-tail, right-tail or two-tailed probability, which is the p-value of a t-test. In critical value mode it gives the t value that cuts off a chosen α, one- or two-tailed, which is the number you compare a test statistic against or plug into a confidence interval.

The t distribution looks like the normal curve but with heavier tails, and it approaches the normal as the degrees of freedom grow; at df = 30 the 97.5th percentile is 2.042 compared with 1.960 for z. The calculator accepts any positive df, including non-integer Welch values, so it matches software exactly rather than the rounded rows of a printed table.

The shaded curve shows the region being measured. A printable t-table is available for exams where a calculator is not allowed, and the one-sample, two-sample and paired t-test pages use this distribution for their p-values.

Frequently asked questions

How do I find the p-value from a t statistic?

Choose probability mode, enter t and the degrees of freedom, and pick the tail that matches your alternative hypothesis. Two-tailed gives 2 × P(T ≥ |t|).

What is the critical t value for 95% confidence?

The 97.5th percentile of t with n − 1 df: 2.262 for df = 9, 2.093 for df = 19, 2.045 for df = 29, approaching 1.960 for very large df.

Can I enter decimal degrees of freedom?

Yes. Welch’s t-test produces non-integer df and the calculator evaluates them exactly.

When does the t distribution become the normal distribution?

Never exactly, but by df = 100 the difference in critical values is under 1%, and many courses switch to z at df = 30 or more.

Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.