It would need to account for the amount of powder in the cartridge, the weight of the bullet, the length of the barrel, the weight of the gun, and the geometry of the gun.
The geometry of the firearm would be the hardest part to account for. Felt recoil involves not only the backward push of the burning propellant, it also involves the upward flip of the gun. The gun's center of gravity, it's moment of inertia, and height of the barrel above the center of gravity, and where your hand makes contact with the firearm would need to be known.
Since everyone's hands are a little different, the formula would not be one size fits all.
I've never seen an attempt at such a formula.
Measuring handgun recoil
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