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Student's t distribution calculator

The t distribution calculator returns tail probabilities and critical values for Student's t on a given number of degrees of freedom — the t-table without the interpolation.

What is Student's t distribution calculator?

Student's t is the sampling distribution of a mean when σ is estimated from the same small sample. Its heavier tails are what make a t-interval wider than a z-interval, and the gap closes as df grows.

Printed t-tables list a handful of df rows and a handful of α columns. This evaluates any df, including non-integer values that arise from Welch's approximation.

When should I use Student's t distribution calculator?

Turning a t statistic into a p-value.
Finding the multiplier for a confidence interval on a mean.
Getting a critical value at a df the printed table skips.

What data does it need?

Distribution parameters, plus a value x, a tail probability p, or both.

What does it report?

For x: the density or exact probability and each tail. For p: the lower, upper and two-tailed critical values.

What does it assume?

None — this evaluates a distribution rather than testing data against one.