Here you go. From an old post explaining sight adjustment formula. Though it is explained for rear sight adjustment, for differential purposes front and rear sight movement amounts to pretty much the same thing. The only difference is that the front sight is just going to be that many inches closer to the target, so the movement of it will be a few thousandths less than the rear to achieve the same result. If you're shooting a 3" group at 100 yards the differential between front and rear movement is MORE than taken up in where you choose to call your center of the group.
Practically and hypothetically speaking; if the calculation calls for you to move the rear sight .107" to get a 1" movement, you would have to move the front sight .105"to get the same result. .002" just isn't enough for our purposes (shooting 3" groups) to be a material difference. Now if you were trying to hit a specific spot on the moon with a laser (like a 1 meter square reflective mirror to measure the Earth-to-moon distance as was left by the Apollo missions), then yeah, those adjustment differentials to the right of the decimal point make a big big difference. But you're lobbing lead from a muzzle loader at 100 yards. Not measuring the difference in distance to the moon to the fraction of an inch over 238,555.38492 miles.
D1 / R1 = D2 / R2
For rear sight adjustments:
D1 is the distance between point of aim and point of impact.
R1 is range from front sight to target.
D2 is the length the rear sight must change by.
R2 is the distance between front and rear sights.
For front sight adjustments:
D1 is the distance between point of aim and point of impact.
R1 is range from rear sight to target.
D2 is the length the front sight must change by.
R2 is the sight radius distance between front and rear sights.
This formula calculates the MAGNITUDE ONLY of the sight height change; refer to the instructions above to find the correct direction for the adjustment (front or rear sight, longer or shorter). Likewise, all distances must be in the same units. That is, if a change in inches to the sight height is desired, and one is shooting on a 100 yard range, then R1 (100 yd) must be converted to inches (100 x 36 = 3600 inches) before using this distance in the equation.
An example: Consider a rifle with a distance between front and rear sights of 26.25 inches, firing on a 50 yard (1800 inches) range, with point of impact 5.3 inches too high on the target, having a front sight blade that is 0.505 inches high mounted in a dovetail. How much must the front sight blade height be changed by to fix this problem? (It will be assumed that the muzzle of the rifle intrudes into the range space for following typical gun range safety protocols, and the rear sight is hence 50 yards from the target.)
D2 = R2(D1/R1) = 26.25(5.3/1800) = 0.077" (magnitude of change to front sight height)
Since the gun is hitting too high, the front sight must be lengthened by this much per the instructions cited previously; hence, the front sight must be replaced with a blade that is 0.505" + 0.077" = 0.582" high. With this correction, the rifle will hit the desired point of impact, all other factors being equal.
