T.INV Function

Excel Functions › Statistical

Excel 2010+ Statistical

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.


Quick answer:
=T.INV(0.95,10) critical t for 95% left area ≈ 1.812

Syntax

=T.INV(probability, deg_freedom)
ArgumentDescription
probabilityRequiredA cumulative probability between 0 and 1 (the area to the left of the returned t-value).
deg_freedomRequiredThe 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.

=T.INV(0.95, 10) // one-tailed 5% critical t ≈ 1.812

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).

=T.DIST(T.INV(0.95,10), 10, TRUE) // round-trips back to 0.95

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

Live demo

Pick a T.INV example to see the formula and its result.

Result:

Practice workbook

📊
Download the free T.INV practice workbook
Every example on this page, ready to open in Excel — plus practice challenges with answers on a separate tab. No sign-up required.

Frequently asked questions

What does T.INV return?
The t-value whose cumulative (left-tail) probability equals the value you supply. It is the inverse of T.DIST(x, df, TRUE).
Why does T.INV sometimes return a negative number?
For a probability below 0.5 the cut-off lies left of center, so the returned t is negative. T.INV(0.5, df) is exactly 0.
How is T.INV different from T.INV.2T?
T.INV is left-tailed: the probability is the area to the left. T.INV.2T is two-tailed: its probability is split evenly between both tails, so it always returns a positive value.
What range can probability take?
Strictly between 0 and 1. Values of 0 or 1 (or outside that range) return an error because the corresponding t-value would be infinite.

Master functions like this in one day

This page covers one function. Our Excel Formulas and Functions class covers the 30 that matter most — live, hands-on, taught by professionals in Dallas–Fort Worth, Houston, Austin, Oklahoma City, Denver, or online.

See the Formulas & Functions Class

Related functions: T.INV.2T · T.DIST · T.DIST.RT · T.DIST.2T · T.TEST · NORM.INV