Powder weight calculates into felt recoil just like bullet weight and velocity. The larger charge expends more energy. It does so more slowly, but the energy is felt none the less. That is why you can get less recoil with a fast powder for the same bullet weight and velocity as with more of a slower powder, although sometimes it can feel snappier.
Unfortunately Handloads.com is down, or I would link to their recoil calculator.
It figures in the same way that bullet weight does: its a product of the mass of the charge and the velocity. Just like the bullet portion of the equation, it relies on Newton's Third Law.
http://kwk.us/recoil.html That's a link to a recoil calculator.
Freely expanding burning smokeless propellant expands at roughly 4000fps regardless of the relative burn rate. The burn rate simply explains how quickly the pressure builds (how quickly the solid mass of the powder converts to the gaseous mass of the combustion products; same mass different form) when that expansion is contained. If the pressure builds quickly (fast burning powder) the initial bullet acceleration is higher and F=MA tells us that higher acceleration means higher force. We already explained the source of the higher force, higher pressure, but Newton's Third Law tells us that the force works in both directions, both pushing the bullet down the bore and pushing the firearm back into the shooter. The higher weight of the firearm means that it's acceleration is much slower given an equal force.
Where the difference between a fast and slow powder comes into play is when you start looking at the plot of pressure over time and figuring the area under the curve. If we could contain unlimited pressure, the fastest powder would be all that we would ever need. You would simply fill the case with fast powder and let'r rip. The pressure would run very high and the large amount of powder would provide a large volume of gas to maintain the pressure at a higher level as the bullet accelerated down the bore providing a larger pressure vessel.
The problem is that there is a limit on the amount of pressure that the firearm and cartridge can safely contain. This is where slower powders come into play. With a slower powder, the gas volume is somewhat regulated and pressure is kept in check. By having the powder burn more slowly, the total amount of combustion product can be increased but the slower rate of conversion allows the bullet to begin down the bore and the chamber volume to expand keeping the pressure in check. A by product of this is that the pressure curve is more gradual and remains at a higher pressure longer. The result is that when compared to a faster burning powder, for the same peak pressure, the area under the pressure curve is greater. The area under the curve represents the total force imparted on the bullet. Higher total force means higher total acceleration and higher resultant velocity.
The more gradual ramping up of the pressure with slower powders also explains the differing characterization of the recoil between two cartridges with the exact same bullet and velocity, one using a fast powder and the other a slower powder. The fast powder has a high initial pressure and a greater initial acceleration resulting in a more "snappy" recoil. The slower powder creates more of a "push" than a "snap" because the initial acceleration is slower.
In general the round with the slower powder will have a larger charge weight. That means an increase in free recoil, but the difference is usually quite small. Perceived recoil is a different story and the more sustained push of the slower powder can make the recoil difference seem like more than it really is. Because we're talking perception, this differs for each person. Firearm design can play a large part in this as well.
