Larger shot have more "Killing Effect" due to two things. 1st the larger diameter punches a bigger hole. 2nd the heavier weight gives greater penetration.
Hole size of spheres is proportional to the square of their diameters. Weight, assuming identical material, is proportional to the cube of their diameters.
In US sizes a #7 should measure .100" in diameter with a # 7 1/2 going .095". Thus (.1/.095) squared = 1.108 so the #7 is approx 11% larger in diameter than a #7 1/2. (.1/.095) cubed = 1.166, thus the #7 is approx 17% heavier. In comparison we are obviously talking of two different shot sizes with the #7 being larger, heavier & thus having more killing power.
British #7 is very close in size to US #7 1/2 , thus having the effect of the smaller size shot. Shot sizes & charge weights need always to consider both adequate penetration of the individual pellets & also adequate pattern density to insure hits on the bird of a given size at anticipated range.
Thusly #8 & #4 shot would not be considered interchangeable on the same birds at the same ranges. The same applies, although to a much lesser degree, when comparing US versus British #7 shot.
