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T.INV Function

Excel 2010+

Summary

The Excel T.INV function returns the left-tailed inverse of the Student's t-distribution, providing the critical t-value for a given probability and degrees of freedom. Essential for hypothesis testing and confidence intervals in statistical analysis.

Syntax

T.INV(probability, deg_freedom)

Parameters

Parameter	Type	Required	Description
probability	`Number`	Yes	A decimal number between 0 and 1 representing the probability associated with the Student's t-distribution
deg_freedom	`Number`	Yes	The number of degrees of freedom (≥ 1); non-integers are truncated

Using the T.INV Function

T.INV is primarily used in statistical analysis to find critical t-values for left-tailed hypothesis tests. It helps determine the threshold where you reject the null hypothesis when the test statistic falls in the left tail of the distribution.

Common T.INV Examples

Basic Left-Tail T-Value

=T.INV(0.75,2)

Returns 0.8164966 - the t-value where 75% of the distribution lies to the left with 2 degrees of freedom.

Hypothesis Testing

=T.INV(0.05,25)

Returns the critical left-tail t-value (-1.708) for α=0.05 with 25 degrees of freedom.

Confidence Interval Lower Bound

=T.INV(0.025,30)

Critical value for 95% confidence interval lower bound with 30 degrees of freedom.

Frequently Asked Questions

It finds the t-value where the area to its left equals the specified probability.

T.INV gives left-tail value; T.INV.2T gives two-tailed critical value (divides probability between both tails).

Yes, but Excel truncates to integer.

Common Errors and Solutions

#VALUE!

Cause: Non-numeric input for probability or degrees of freedom

Solution: Ensure both arguments are valid numbers

#NUM! (probability issue)

Cause: Probability ≤ 0 or > 1

Solution: Use probability between 0 (exclusive) and 1 (exclusive)

#NUM! (degrees of freedom)

Cause: Degrees of freedom < 1

Solution: Use integer ≥ 1

Notes

If deg_freedom is non-integer, Excel truncates it toward zero
Probability must be greater than 0 but less than 1
Negative results indicate left-tail values below zero
Consider T.INV.2T for two-tailed tests

Compatibility

Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2007, Excel 2003, Earlier versions

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+