# Student's t-distribution

I have two functions that provide an implementation of the t-distribution.

A webpage with a Javascript algorithm. The algorithm takes two input x-value and degrees_of_freedom.

Excel's TInv function. The function also takes two inputs: probability and degrees_of_freedom.

Can you give me the relation between probability and x-value? I have doubts that the two methods calculates the same thing.

The first takes a value on the x-value and degrees of freedom and reports the amount of probability to the left of the x-value. If you're familiar with calculus, this is the equivalent of taking the integral of the Student's t probability density function over the interval $(-\infty,x]$. If you're familiar with statistics, this is the Student's t cumulative density function evaluated at $x$ for some degrees of freedom.
The second does the inverse, taking some probability and returning the corresponding x-value. In statistics, this is called the quantile function.