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Formula follows. There are ways to do this in a single step, but I don't have the proper formula for that. So basically follow these three steps and it'll work it out for you.
Typically lighter bullet means less kick, to give you a brief answer.
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1. Calculate recoil impulse:
I=(WB * VB + 4000 * WC)/225400
Where
WB=wt of bullet in grains,
VB=velocity of bullet in fps, and
WC is the wt of the powder charge in grains. (I is in lbs/sec)
2. Calculate the velocity of the recoiling gun:
VG=32.2 * I / WG
Where
WG is the wt of the gun in lbs.,
32.2 is the acceleration due to gravity, and
I is the recoil impulse from calculation #1
3. Calculate the free recoil energy of the gun in ft lbs.
EG=WG * VG^2 / 64.4
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