r = sqrt(         (t^2)  /  (t^2 + (n-2))         )

t = (r * sqrt(n-2))/( sqrt(1-r^2) )

verified to be within rounding error by ajs using graphpad-quickcalcs, nov 2007

warning1: the T to R (but not the R to T) formula will remove the sign; you can maintain sign by multiplying the result of the conversion by (t / abs(t))
warning2: for multiple regression, ancova, or partial correlations, replace "n" with the df appropriate to the predictor and covariates; eg, for a single predictor and a single cov, df=n-2-1