T Distribution Calculator
Compute cumulative probabilities, critical t-values, and p-values for hypothesis testing with a t-statistic.
Category: Statistics
About this tool
What Is the t distribution? T Distribution Calculator. The t distribution calculator converts between a t-value and a probability the way t-tables do, but without the rounding gaps: give it t or a probability and it returns the other exactly, for any degrees of freedom. Helmert's and Student's t distribution describes sample means when the population standard deviation is unknown. With small samples its tails are fatter than the normal's; as degrees of freedom grow it converges to the normal. The calculator pairs two integrations: the cumulative distribution function gives the area under the curve up to any t, and the inverse CDF (critical value) finds the t that produces a target two-tailed probability such as 0.05. P(T ≤ t) via numerical CDF; critical value t = CDF⁻¹(p). How to Use Enter the degrees of freedom and a t-value to get the one- and two-tailed probabilities. Or enter a target probability in percent to receive the matching critical t. Read the two-sided conclusion directly in the results. Worked Example With df = 10 and t = 2.228, the tool returns a two-tailed probability of about 5.0%, the classic 95% confidence critical value. Flipping it: entering 5% probability at df = 10 gives back t ≈ 2.228. Common Use Cases two-sample mean comparisons confidence intervals with small samples regression coefficient significance A/B test decisions Important Notes Probabilities p