Tony - Memphis
Well, I don't know a particular formula, but I wrote a program to calculate such things many years ago. I used it for other stuff. It used to be available for download on the Creek. You might try segment calculators for bowl turning - same thing. I think there are some other free calculators out there. Might even be a spreadsheet or two. I'd offer mine, but it has been so long, I don't know where the code is!
Tony (not a programmer, but a hack)