Student t Distribution Calculator
Calculate probabilities, critical values, and quantiles for the Student t distribution with interactive PDF and CDF charts.
The Student t distribution is the workhorse of small-sample inference. It appears whenever you estimate a population mean from limited data with unknown variance, producing wider intervals than the normal to account for that extra uncertainty.
Use this calculator to find t critical values, compute tail probabilities for hypothesis tests, and visualize how degrees of freedom control the heaviness of the tails.
Launch the Student's t Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhat is the Student t distribution used for?
It is used for hypothesis tests and confidence intervals when the population standard deviation is unknown and the sample size is small.
How do degrees of freedom affect the t distribution?
Fewer degrees of freedom produce heavier tails and wider intervals. As degrees of freedom increase, the t distribution converges to the standard normal.
How do I find a t critical value for a two-tailed test?
Set the quantile to 1 − α/2 (for example, 0.975 for a 5% significance level) and read the corresponding t value.