The gauge of a shotgun barrel was originally determined by the number of identically-sized lead balls that have the same diameter as the bore, and weigh one pound. Example: Let's say the bore of a 20 gauge is .6 of an inch. It would take 20, six tenths of an inch lead balls, to weigh 1 pound. Using the same numbers, if one were to build a gun with a bore of .675 it would take 16 lead balls that size to weigh 1 pound--- thus a 16 gauge. Oops !! - what about a 410? Truth is a 410 is not actually a gauge. It is a caliber... .410 inches bore. Applying the math to this would make a 410 shotgun actually a 67 gauge.... so next time you go to buy your 410 shells ask for some 67 gauge shells and see what happens :-).
If you want to play with this (lots of time on your hands) here is some of the math.
* Formula for volume of a sphere is (4/3) *( pie [3.1416]) * (R cubed).
* "R" is radius or 1/2 the diameter which in this case would represent the bore of a shotgun.
* Approx. 2.4 cubic inches of lead weighs one pound.