What is the a measure related to the diameter of the bore and the size of the shot shell designed for the bore?

The measure related to the diameter of the bore and the size of the shotgun shell is known as "gauge." The gauge is determined by the number of lead balls of the bore diameter that equal one pound; for example, a 12-gauge shotgun has a bore diameter that allows for 12 lead balls of that diameter to weigh one pound. The smaller the gauge number, the larger the bore size. This system is commonly used to classify shotguns and their corresponding ammunition.