The invT( Command

Command Summary

Calculates the inverse of the cumulative Student's t-distribution function with degrees of freedom ν.

Command Syntax

invT(probability, ν)

Menu Location


  1. 2ND DISTR to access the distribution menu
  2. 4 to select invT(, or use arrows.

Calculator Compatibility

TI-84+/SE (OS 2.30 or greater)

Token Size

2 bytes

invT( is the inverse of the cumulative Student t distribution function: given a probability p and a specified degrees of freedom v, it will return the number x such that tcdf(E-99,x,v) is equal to p



invT( is meant for use with so-called "one-tailed' tests; for two-tailed tests, the proper expression to use (corresponding to the inverse of tcdf(-x,x,v)) is invT(.5(1+p),v)


Unlike the tpdf( and tcdf( commands, the invT( command does not have a closed-form formula. However, it can be expressed in terms of the inverse incomplete beta function.

For one degree of freedom, invT( is expressible in terms of simpler functions:

\begin{align} \operatorname{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right) \end{align}

Related Commands


Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Noncommercial 2.5 License.