TINV function

Returns the two-tailed inverse of the Student's t-distribution.

 Important   This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

For more information about the new functions, see T.INV.2T function or T.INV function.



The TINV function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

  • Probability     Required. The probability associated with the two-tailed Student's t-distribution.
  • Deg_freedom     Required. The number of degrees of freedom with which to characterize the distribution.


  • If either argument is nonnumeric, TINV returns the #VALUE! error value.
  • If probability <= 0 or if probability > 1, TINV returns the #NUM! error value.
  • If deg_freedom is not an integer, it is truncated.
  • If deg_freedom < 1, TINV returns the #NUM! error value.
  • TINV returns that value t, such that P(|X| > t) = probability where X is a random variable that follows the t-distribution and P(|X| > t) = P(X < -t or X > t).
  • A one-tailed t-value can be returned by replacing probability with 2*probability. For a probability of 0.05 and degrees of freedom of 10, the two-tailed value is calculated with TINV(0.05,10), which returns 2.28139. The one-tailed value for the same probability and degrees of freedom can be calculated with TINV(2*0.05,10), which returns 1.812462.

 Note    In some tables, probability is described as (1-p).

Given a value for probability, TINV seeks that value x such that TDIST(x, deg_freedom, 2) = probability. Thus, precision of TINV depends on precision of TDIST. TINV uses an iterative search technique. If the search has not converged after 100 iterations, the function returns the #N/A error value.


The workbook below shows examples of this function. Inspect them, change existing formulas, or enter your own formulas to learn how the function works.

To work more in-depth with the example data in Excel, download the embedded workbook to your computer, and then open it in Excel.

Applies to:
Excel 2013, Excel Online