After the gauge you have to know the density, to determine mass per unit length, then string length and tension determines pitch of fundamental.
Also end conditions, but these are pretty much the same for all strings. It's an odd combo of fixed and free mode. They aren't really free and they aren't really fixed either. I think they usually bodge it and consider the end to be free some distance away from the nut and bridge. Otherwise you would have to consider the stiffness in the string at the ends.