Student t distribution calculator
Enter degrees of freedom and interval bounds. The calculator returns both tail probabilities, the area between the bounds and a distribution graph.
Your numbers stay in this browser. No account or upload to the server is needed.
How do I use this page?
- Enter an integer number of degrees of freedom ν.
- Enter lower bound a and upper bound b.
- Read P(T≤a), P(a≤T≤b), P(T≥b) and inspect the shaded graph.
Method and worked example
The Student t distribution is symmetric around zero and has heavier tails than the normal distribution. Its shape depends on degrees of freedom ν.
The cumulative probability uses the regularised beta function. For t≥0: F(t)=1−½ Iₓ(ν/2,1/2), where x=ν/(ν+t²). Symmetry handles t<0.
As ν increases, the distribution approaches the standard normal distribution. The tool calculates model areas; it does not verify assumptions of a statistical test.
Example: with ν=10, bounds −2.228 and 2.228 contain about 95% of the distribution, leaving about 2.5% in each tail.