The Excel T.INV function returns the left-tailed inverse of the Student's t-distribution — the t-value for which the cumulative probability equals a given amount.
Syntax
| Argument | Description | |
|---|---|---|
probability | Required | A cumulative probability between 0 and 1 (the area to the left of the returned t-value). |
deg_freedom | Required | The degrees of freedom (a positive integer). |
How to use it
T.INV is the inverse of T.DIST(…, TRUE): give it a left-tail probability and it returns the t-value that cuts off that area. It is how you look up a one-tailed critical value.
Because the distribution is symmetric, a probability below 0.5 returns a negative t. For a two-tailed critical value, use T.INV.2T (or call T.INV with 1−alpha/2).
Confidence intervals: for a 95% one-sided bound with 10 degrees of freedom, T.INV(0.95,10) gives the multiplier. For a two-sided 95% interval you want T.INV.2T(0.05,10) instead.
Try it: interactive demo
Pick a T.INV example to see the formula and its result.
Practice workbook
Frequently asked questions
What does T.INV return?
T.DIST(x, df, TRUE).Why does T.INV sometimes return a negative number?
How is T.INV different from T.INV.2T?
What range can probability take?
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