T.INV.2T Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel T.INV.2T function returns the two-tailed inverse of the Student's t-distribution — the positive t-value that leaves a given probability split equally between both tails.


Quick answer:
=T.INV.2T(0.05,10) two-tailed 5% critical t ≈ 2.228

Syntax

=T.INV.2T(probability, deg_freedom)
ArgumentDescription
probabilityRequiredThe total two-tailed probability, between 0 and 1 (split evenly across both tails).
deg_freedomRequiredThe degrees of freedom (a positive integer).

How to use it

T.INV.2T answers “what critical t leaves probability in the two tails combined?” — the value you use for a two-sided confidence interval or a non-directional t-test.

=T.INV.2T(0.05, 10) // 95% two-sided critical t ≈ 2.228

It always returns a positive number, and it relates to the left-tailed T.INV by T.INV.2T(p, df) = T.INV(1 − p/2, df).

=T.INV(1-0.05/2, 10) // same ≈ 2.228

Pick the level by alpha: for a 95% two-sided interval pass 0.05; for 99% pass 0.01. The function does the “divide alpha between the tails” bookkeeping for you.

Try it: interactive demo

Live demo

Pick a T.INV.2T example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

What does T.INV.2T return?
The positive t-value that leaves the supplied probability split equally between the two tails — i.e. the two-sided critical value for that significance level.
How does T.INV.2T relate to T.INV?
T.INV.2T(p, df) = T.INV(1 − p/2, df). The two-tailed version puts half the probability in each tail, so it converts to a left-tail lookup of 1 − p/2.
What probability do I pass for a 95% interval?
Pass the significance level alpha, which is 0.05 for 95% confidence (0.01 for 99%). The function returns the matching critical t.
Does T.INV.2T ever return a negative number?
No. Because the probability is shared symmetrically between both tails, the result is always the positive critical value; apply ± yourself for the lower bound.

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