The Good News; There is a Formula

The Bad News... its slightly complex, although it is really just trigonometry, there's a lot of trigonometry. This is especially true if you account for the fact that the Radius of a Planet is not constant, even when you don't account for Mountains and Stuff, the planet tends to be wider around the equator. Of course, for most mapping purposes you can be forgiven for just assuming the Radius is constant when not modified by Mountains/Valleys and estimating.