The Ideal Gas Law PV=nRT states pressure is inversely proportional to volume. If we assume nRT is a constant c then P = c/V.

If we let c equal the chemical reaction of the propellant and call it 1000;

then for a .300 cal that has traveled 5” down the barrel, P = 1000/(.300Pi*5) = 210

for a .458 cal P = 1000/(.458Pi*5) = 140

For the same gas generated by the propellant, the pressure is less in a big bore. Conversely, to reach the same velocity, more propellant is needed.