Kinetic energy (Ke) = 1/2 * M * V * V or, in the case of using weight instead of mass...
Ke = m * v2 / (2 * 32.1739 * 7000) (where m is bullet weight in grains)
See: http://en.wikipedia.org/wiki/Muzzle_enegry
.45 230gr @ 725 FPS = 166.75 PF, but...
230 * 725 * 725 / (450,434.6) = 268.39 ft. pounds
9mm 115gr @ 1150 FPS = 132.25 PF, but...
115 * 1150 *1150 / (450,434.6) = 337.65 ft. pounds!
That's about 25% more kinetic energy in your hand, but why does the 9mm (at minor PF) feel softer??? Well...
Power Factor = M * V = momentum at muzzle (or shortly thereafter), but...
Perceived recoil really has much more to do with impulse. Impulse is force applied over a specified time period. This explains it well...(impulse-momentum equation).
So, to us shooters, the heavier bullet has more stationery "momentum" to overcome by exerting force, but also more time in the barrel (due to lower velocities) to achieve the desired terminal momentum (PF). So, this should explain now how two identical PF loads have different perceived recoil...
.45 230gr @ 725 FPS = .40 185gr @ 901 FPS = 166.75 PF BUT (last one, I promise)...
Since Force = M(ass) * A(cceleration) you have to create (901/725=) 24.28% more acceleration with only ((185/230)-1=) 19.56% less mass. Therefore, the force is greater with the .40 185gr projectile!
Now, don't you feel smarter!?
Ehh..I thought I was but now...........