LC,
Wikipedia provides the formula which you should be able to find via Google or other seach engine. The formula is pretty complicated.
For most of us non-PhD's Bruce Buck provides the following from Shotgun Report:
"Does aftermarket (not factory) backboring have any benefit at all? You can bet your Junior Technoid magic slide rule ring that it does. While aftermarket backboring may not reduce recoil or improve patterns, it sure reduces weight. If the barrels on your gun feel too heavy and unresponsive, you may be able to put them on a diet. Most standard barrels have a wall thickness of around .040". This is a lot of meat and might be substantially reduced. On a standard 30" set of barrels, backboring .010" will reduce barrel weight by 2.77 ounces. A .020 backbore will take off a monumental 5.58 ounces. A change of 3 ounces is a lot, so go easy. Check first with your gunsmith. He will know what is safe. Be aware, however, that aftermarket backboring will void any factory warrantee. Briley charges about $150 per tube for backboring."
Regards,
Bruce Buck
Shotgun Report's Technoid