# Recoil energy of a shotgun

Recoil energy calculator This program calculates the recoil energy when you shoot a shotgun. You need to know the load weight in ounces, the muzzle velocity. (i.e. 1 1/8th ounce at 1145 fps) and the weight of your gun in pounds. If you know the weight of the wad and the number of grains of powder, you can also enter those numbers, otherwise average values of 33 grains for the wad and 18 grains for the powder will be used. The weight of the wad and powder do not typically change the result by a significant amount.
All numbers must be entered as decimal values. For your convenience the following list of common loads are provided.

3/4 oz. = 0.75 oz.
24 gram = 0.847 oz.
7/8 oz. = 0.875 oz.
1.0 oz. = 1.0 oz. (yes this is obvious but this is the internet)
1 1/8 oz. = 1.125 oz

1 1/4 oz. = 1.25 oz.
1 1/2 oz. = 1.5 oz.
1 5/8 oz = 1.675 oz.
1 3/4 oz. = 1.75 oz.
1 7/8 oz. = 1.875 oz.

 Weight of Shot (oz.) Velocity in Feet Per Second (FPS) Weight of gun in lbs. Weight of wad in grains (optional) Amount of powder in grains (optional) Foot Pounds of Recoil Energy

Sweat and Bother

The three primary variables that influence recoil energy are the amount of shot that goes out the barrel, the velocity of the shot and the weight of the gun. Increase the amount of shot or the velocity of the shot and the recoil energy increases. Increase the weight of the gun and the recoil energy decreases.

A little bit of physics
There are two basic physics principles involved in this problem ... conservation of momentum and calculation of kinetic energy. Complicating the issue is that we use ounces for shot weight, grains for powder weight, lots of different units for wad weight and physics like mass not weight.

Before you shoot a shotgun the gun and the shot shell pellets are both at rest. After you shoot the pellets/wad/powder goes out the barrel and the gun goes in the other direction. The key here is momentum which is mass times velocity. So although the velocity of the pellets is large, their mass is small compared to the mass of the gun. The key equation here is:

Where the left side is the mass and velocity of the gun and the right is the mass and velocity of the shot pellets, wad and powder gases. The velocity of the shot and wad is given to us by the manufacturers. The velocity of the powder gases is a little more complicated. There are a number of values for the velocity of the gases. The most commonly used one is 4,700 ft/s. Another estimate is 1.7 times the muzzle velocity of the shot. For this calculator I am using 4,700 ft/s. The difference here is one of a few percent, not very significant.

Since we know the mass/weight of the shot, the mass of the powder, the muzzle velocity and the mass/weight of the gun we can calculate the recoil velocity of the gun.

Once we have the recoil velocity of the shotgun we can calculate the kinetic energy of the gun. This is the "free" recoil energy. The recoil energy is calculated as:

Energy = 1/2 mgunvgun2

So we now have all we need to calculate the recoil energy of a shotgun if we know the weight of the gun, the amount of shot, the velocity of the shot, the weight of the wad and the amount of powder. If you don't know the weight of the wad or the weight of the powder I put in average values. No worries as these two values won't change the final answer by a significant amount.

The other problem is to do a bunch of conversions. There are 16 ounces to a pound and 7,000 grains to a pound. Getting from weight to mass requires that we convert pounds to slugs ... on earth there are about 32 lbs to a slug.

So the final equation for calculating recoil energy is:

Recoil Energy = (mshotvshot + mwadvwad + 4,700 * mpowder) 2/64.348* mgun

where in the numerator we have the mass of the shot times the velocity of the shot plus the mass of the wad times the velocity of the wad plus the velocity of the powder (4,700 ft/s) times the mass of the powder. That quantity is squared. It is divided by the mass of the gun. The 64.348 does all of the conversions (lbs to slugs*2 for kinetic energy).