The gauge of a shotgun is the measurement of the inside width of the barrel. The number refers to the weight, in fractions of a pound, of the largest perfectly spherical ball of lead that could fit into the barrel of the shotgun. A 12 gauge, for example, can fit a ball of lead weighing onetwelfth of a pound into its barrel. The gauge can usually be found written on the rear of the gun barrel, but if not, you can calculate it.
Things You'll Need
 Calipers measuring fractions of an inch accurate to three decimal places
 Calculator

Position the tips of the caliper's nose into the end of the gun barrel and open across the widest point to find the internal diameter. Keeping the body of the calipers at right angles to the opening, move the the calipers around until you find the maximum reading. As an example, a measurement you might find is .725 in.

Note the reading to at least three decimal places and cube the number, i.e., multiply diameter x diameter x diameter. Make a note of this number, which is the cube of the diameter. Using our example .725 cubed is 0.381078125.

Divide 7,000 by the cube of the diameter. Divide this number by 1501.339.
To continue with our example, 7,000 divided by 0.381078125 is 18368.93682.
Then, 18368.93682 divided by 1501.339 is 12.23503607.

Round your answer to the nearest whole number to get the gauge of the shotgun.
To finish our example, 12.23503607 rounds to 12, so a shotgun with a barrel diameter of .725 in. is a 12 gauge.
Tips & Warnings
 A shotgun with a barrel diameter of .410 is always referred to as a 410, whether you are talking about gauge or bore.
 You need to make really sure that the gun is not loaded when performing the measurement across the opening of the barrel. Doublecheck every time and adhere to all the other safety precautions which apply when handling a firearm.
References
 "Fine Gunmaking: Double Shotguns"; Steven Dodd Hughes; 1998
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