I never thought about the "units" for the BC.... I'm guessing it's a dimensionless number like most Coefficients are.... Things like Drag and Lift Coefficients in Aerodymnamics are the same in Imperial and Metric systems, so must be dimensionless.... The theoretical BC is the Sectional Density (SD) divided by a "shape factor".... For a sphere, that is supposed to be 1.55.... That is why larger calibers tend to have better BCs because the SD is often greater.... No substitute for shooting and measuring it, though....

Bob