RE: Shotgun question
One problem, Hog. The barrel diameters vary quite a bit among the manufacturers.
You are correct that the amount of choke constriction in a barrel is the difference between its bore diameter and the constriction at its muzzle. The best way to measure both is with a dial caliper as you showed. In a 12 gauge as an example, while standard bore diameter is supposed to be in the neighborhood of .729 to .730 inch, barrels from various makers can range anywhere from .720 to .735 inch, and those that have been backbored can be even larger. Assuming that the correct amount of constriction for, say, Full choke for the 12 gauge is .040 inch, it is easy to see how actual inside diameter at the muzzle can vary from .680 to .695 inch for that designation.
BNS, since you probably don't want to buy a caliper to measure one time, visit a gunsmith that works on shotguns and he can tell you the amount of constriction.