# Calculate the percentile from a T-score

Is it possible to calculate the percentile from a T-score?

If yes, what formula can be used for it, and what other variables (e.g. standard deviation, degrees of freedom, etc.) are needed for it?

• Welcome to stats.SE! Please take a moment to view our tour. Are you seeking to calculate the percentile of the T-score relative to other T-scores or are you hoping to calculate a percentile for your distribution based upon the T-score? – Tavrock Feb 28 '17 at 1:54

The formula for this is as follows, where $\nu$ is the degrees of freedom, $t^{2} < \nu$, and $_{2}F_{1}$ is a hypergeometric function.
$\int^{t}_{-\inf} f(u) du = \frac{1}{2} + t [ \frac{\Gamma(\frac{\nu + 1}{2})}{\sqrt{\pi\nu}\Gamma(\frac{\nu}{2})}] [ _{2}F_{1}(\frac{1}{2}, \frac{\nu + 1}{2}; \frac{3}{2}; -\frac{t^2}{\nu})]$
This can be easily done in R using pt().