Afaik, the FOV stays the same, no matter what the camera distance from the player is.
It depends mostly (if not completely) on the aspect ratio of the WorldFrame. So, players with a widescreen have a higher FOV than players with 4:3.
I needed to calculate it for my 3D coordinate addon
Coordinator Around lines 94/95 is the part of it, although it does not calculate the FOV directly, but it relates to it.
Just try to experiment a bit with the aspect ratio.
Btw, I planned to rewrite Coordinator very similar to your idea, since Blizz' disabled the camera-cVars. I need my 3D-quest target for leveling :/