The error function erf(x) and the normal distribution Φ(x) are essentially the same function. The former is more common in math, the latter in statistics. I often have to convert between the two.
It’s a simple exercise to move between erf(x) and Φ(x), but it’s tedious and error-prone, especially when you throw in variations on these two functions such as their complements and inverses. Some time ago I got sufficiently frustrated to write up the various relationships in a LaTeX file for future reference. I was using this file yesterday and thought I should post it as a PDF file in case it could save someone else time and errors.