Convert from button measure to caliber

Unit Definition (button measure)
The button measure is a unit of distance equal to 1/40 inch (0.635 millimeter), used to measure the thickness of buttons.

Unit Definition (caliber)
The caliber is a unit used to express the bore diameter of a gun. Traditionally, the diameter is stated in inches, so that ".22 caliber" refers to a pistol having a bore of 0.22 inches (5.588 mm). So the caliber is actually equivalent to the inch. The usage of the term "caliber" is actually now in decline, because bore diameters of many guns are now stated in millimeters. "Caliber" is the American spelling; elsewhere the unit is often spelled "calibre."