Recoil Energy Calculator finds free recoil energy, recoil velocity and impulse from bullet weight, muzzle velocity, powder charge and gun weight of a rifle, shotgun or pistol load.
Weigh the gun the way you shoot it, with scope, sling and a full magazine.
Compare and Target
Load B is fired from the same gun. Its powder gas velocity follows its own muzzle velocity.
Recoil at Other Gun Weights
| Gun Weight | Energy | Velocity | Change |
|---|---|---|---|
| 6 lb | 22.02 ft-lbf | 15.37 fps | +33.3% |
| 7 lb | 18.87 ft-lbf | 13.17 fps | +14.3% |
| 8 lb | 16.51 ft-lbf | 11.53 fps | Yours |
| 9 lb | 14.68 ft-lbf | 10.24 fps | −11.1% |
| 10 lb | 13.21 ft-lbf | 9.22 fps | −20% |
| 11 lb | 12.01 ft-lbf | 8.382 fps | −27.3% |
Momentum Balance and Steps
- Vc = 1.75 × Vb = 1.75 × 2,800 = 4,900 fps
- Vf = (Mb × Vb + Mc × Vc) ÷ (7000 × Mf), with Mb and Mc in grains and Mf in pounds
- Vf = (150 × 2,800 + 46 × 4,900) ÷ (7000 × 8) = 11.525 fps
- Er = Mf × Vf² ÷ (2 × 32.174) = 8 × 11.525² ÷ 64.348 = 16.51 ft-lbf
- Ir = Mf × Vf ÷ 32.174 = 8 × 11.525 ÷ 32.174 = 2.866 lbf·s
What the Recoil Energy Calculator Works Out
The Recoil Energy Calculator takes bullet weight, muzzle velocity, powder charge and firearm weight. It returns free recoil energy in ft-lbf or joules, plus the recoil velocity and recoil impulse behind that number.
The loaded example is a 150 gr bullet at 2,800 fps over 46 gr of powder in an 8 lb rifle. That comes to 16.51 ft-lbf, or 22.39 J, with the gun moving back at 11.53 fps and an impulse of 2.866 lbf·s.
The same bullet leaves with about 2,611 ft-lbf, which you can check in the Bullet Energy Calculator. Gun and bullet share the same momentum, but the gun is far heavier, so it keeps under 1% of the kinetic energy.
Firearm Type sets how fast the powder gas is assumed to leave the muzzle, with separate choices for rifles, shotguns, handguns and black powder. Compare and Target holds a second load fired from the same gun, a brake or suppressor cut, and a recoil figure you want to reach, which defaults to 15 ft-lbf.
Recoil Energy Formula From SAAMI
Recoil is conservation of momentum. The gun goes back with the momentum that the bullet and the powder gas carry forward. SAAMI publishes the method in its Gun Recoil Formulae technical sheet, and the recoil velocity comes first.
$$V_f = \frac{M_b \times V_b + M_c \times V_c}{7000 \times M_f}$$
Here M_b and M_c are the bullet and powder charge in grains, V_b and V_c are the bullet and powder gas velocities in fps, and M_f is the firearm weight in pounds. The 7000 converts grains to pounds.
The recoil energy formula is the kinetic energy of the gun at that velocity. The firearm weight is divided by gravity, 32.174 ft/s squared, to turn pounds into mass. SAAMI rounds it to 32.17.
$$E_r = \frac{M_f \times V_f^2}{2 \times 32.174}$$
Recoil impulse is the gun’s momentum, and it equals the forward momentum of everything that left the barrel. Dividing by gravity again gives it in pound-force seconds.
$$I_r = \frac{M_f \times V_f}{32.174}$$
Powder gas is hard to weigh and harder to clock. SAAMI treats the gas weight as the charge weight and sets its speed as a multiple of muzzle velocity, which is what the Firearm Type list applies.
| Firearm type | Powder gas velocity | Gas speed at 1,200 fps |
|---|---|---|
| High powered rifle | 1.75 x muzzle velocity | 2,100 fps |
| Shotgun, average barrel | 1.50 x muzzle velocity | 1,800 fps |
| Shotgun, long barrel | 1.25 x muzzle velocity | 1,500 fps |
| Pistol or revolver | 1.50 x muzzle velocity | 1,800 fps |
For the loaded example, the Recoil Energy Calculator sets the gas at 1.75 x 2,800 = 4,900 fps. Bullet momentum is 150 x 2,800 = 420,000 and gas momentum is 46 x 4,900 = 225,400, both in grain-fps. Their sum over 7000 x 8 gives 11.525 fps.
Energy is then 8 x 11.525 squared, divided by 64.348, which is 16.51 ft-lbf. The Momentum Balance and Steps panel prints these same lines with your own numbers, in US or metric units.
Why Two Calculators Disagree
Most disagreement between recoil tools comes from one input, the powder gas velocity. SAAMI scales it with muzzle velocity. Older formulas use one fixed speed for every load, often 4,000 fps for smokeless powder.
The loaded 150 gr example shows how far that one choice moves the answer. Bullet, charge and rifle weight stay the same in every row, and only the powder gas velocity changes.
| Powder gas velocity | Recoil energy | Recoil velocity |
|---|---|---|
| 4,000 fps fixed | 14.46 ft-lbf | 10.79 fps |
| 4,900 fps (SAAMI rifle, 1.75 x 2,800) | 16.51 ft-lbf | 11.53 fps |
| 5,000 fps fixed | 16.75 ft-lbf | 11.61 fps |
| 5,200 fps fixed | 17.23 ft-lbf | 11.77 fps |
That is a 19% spread on one load. If your figure does not match a chart or another Recoil Energy Calculator, pick Custom Gas Velocity and enter the speed that source uses. The result should then line up.
Black powder gas leaves much slower than smokeless gas, so a black powder load run on the rifle factor reads high. The Black Powder type holds the gas at 2,250 fps, a commonly used average, and takes the full charge by weight in grains.
The effect is large. The loaded 150 gr example drops from 16.51 to 10.86 ft-lbf when only the firearm type changes to Black Powder. Real black powder charges are far heavier than smokeless ones, so enter the true charge and velocity of your load.
Slow, heavy loads show the same effect in reverse. A military 7.62 mm load of 10.1 g at 845 m/s with 3.1 g of powder in a 4.5 kg rifle gives 19.12 J on the SAAMI factor. A fixed 1,575 m/s gas speed gives 20.0 J.
Is .45-70 High Recoil Next to .30-30?
It depends on which .45-70 you load. Sierra lists the cartridge at three pressure levels, for Trapdoor Springfields, for the Winchester 1886 and for the Marlin 1895. The table runs Sierra’s 300 gr hunting loads through the Recoil Energy Calculator on the SAAMI rifle factor, all in a 7.5 lb gun.
| Load | Bullet and velocity | Powder charge | Recoil energy | Recoil velocity |
|---|---|---|---|---|
| .30-30 Winchester | 150 gr at 2,250 fps | 31.8 gr | 9.05 ft-lbf | 8.81 fps |
| .45-70, Trapdoor level | 300 gr at 1,650 fps | 36.0 gr | 15.17 ft-lbf | 11.41 fps |
| .45-70, 1886 level | 300 gr at 1,800 fps | 41.0 gr | 18.94 ft-lbf | 12.75 fps |
| .45-70, Marlin 1895 level | 300 gr at 2,200 fps | 54.3 gr | 31.94 ft-lbf | 16.55 fps |
| .308 Winchester | 150 gr at 2,900 fps | 44.8 gr | 18.55 ft-lbf | 12.62 fps |
So a .45-70 does have more recoil than a .30-30 at every level. The mild Trapdoor load is about 1.7 times the .30-30, and the full Marlin load is about 3.5 times. In between, the 1886 load sits right beside a .308.
Whether .45-70 is too much recoil comes down to the rifle weight. The Marlin-level load needs a gun of about 12 lb to fall to 20 ft-lbf, which the Target Recoil Energy field works out for any load.
The complaint is as old as the cartridge. Sierra’s .45-70 Government data notes that the original 500 gr load kicked too hard in the light cavalry carbine, so the arsenal issued a 405 gr bullet over 55 gr of black powder.
The charges above come from Sierra’s manual pages for the .45-70, the .30-30 Winchester and the .308 Winchester. They are here as recoil inputs. Take loading data from the manual itself.
Shotgun Recoil Energy Calculator Setup
A shotgun recoil energy calculator needs one thing a rifle tool does not, the wad. The wad leaves with the shot, so its weight belongs in the ejecta. Picking either shotgun type renames the first field to Shot + Wad Weight.
SAAMI’s own worked example is a 12 gauge load. It has 1 1/4 oz of shot, which is 546.9 gr, plus 43 gr of wads, at 1,275 fps over 33.4 gr of powder in a 7 lb gun. SAAMI prints 30.22 ft-lbf.
Enter 589.9 gr, 1,275 fps, 33.4 gr and 7 lb in the Recoil Energy Calculator under Shotgun, Average Barrel. The result is 30.17 ft-lbf at 16.65 fps. The 0.05 gap is rounding inside SAAMI’s printed steps. The long barrel factor gives 29.39 ft-lbf.
Powder gas is only 7.8% of the impulse in that load, against 34.9% in the rifle example. That is why a 12 gauge shotgun recoil calculator barely moves with barrel type, while payload and gun weight move it a lot.
Chuck Hawks’ shotgun recoil table shows the range. A 12 gauge 1 oz load at 1,180 fps in a 7.5 lb gun is 17.3 ft-lbf. A 1 1/8 oz target load is 23.0, and a 3 inch 1 5/8 oz magnum is 52.0 ft-lbf.
Recoil Velocity, Impulse and Felt Recoil
Recoil energy says how hard the blow is. Recoil velocity says how sudden it is. Chuck Hawks puts about 15 ft-lbf and 10 fps as the upper comfort level from the shoulder, and reports that over 20 ft-lbf most shooters start to flinch.
Chuck Hawks also cites a 15 fps recoil velocity limit from the 1929 British Textbook of Small Arms. The result note under the cards flags a load that passes it, along with the 15 and 20 ft-lbf marks.
The Equal Free-Fall Drop Height row turns velocity into something you can picture. A gun recoiling at 11.53 fps hits your shoulder as fast as the same gun dropped from 24.8 inches, the speed a free fall from that height produces.
Recoil impulse is the one figure that gun weight cannot change. A heavier rifle takes the same 2.866 lbf·s and turns it into less speed and less energy. Handgun loads are better compared on impulse and velocity, so the 15 and 20 ft-lbf marks are not applied to them.
No felt recoil calculator can be built from these four inputs alone, and the Recoil Energy Calculator does not try. Free recoil treats the gun as floating with nothing behind it. Stock shape, recoil pad, action type and your stance all change how the same energy lands, and gas-operated actions spread it over more time.
A figure like 1,200 g of recoil is a different measurement. It is acceleration, and it appears on optics as a shock rating. ZEISS, for one, tests its riflescopes with over 800 shocks at up to 1,500 g.
Acceleration is recoil velocity divided by the time it takes to build. The 3.513 m/s of the loaded example, reached in one millisecond, averages about 358 g. The tool does not ask for that time, so it reports no g figure.
What Reduces Recoil the Most
High recoil comes from a heavy payload, high velocity, a big powder charge or a light gun. Gun weight is the surest lever, because recoil energy falls in direct proportion to it. The Recoil at Other Gun Weights table reruns your load in steps around your own gun. For the loaded example it reads as follows.
| Gun weight | Recoil energy | Recoil velocity | Change |
|---|---|---|---|
| 6 lb | 22.02 ft-lbf | 15.37 fps | +33.3% |
| 7 lb | 18.87 ft-lbf | 13.17 fps | +14.3% |
| 8 lb | 16.51 ft-lbf | 11.53 fps | Yours |
| 9 lb | 14.68 ft-lbf | 10.24 fps | -11.1% |
| 10 lb | 13.21 ft-lbf | 9.22 fps | -20% |
The gun weight card answers the reverse question. The same load reaches 15 ft-lbf at 8.807 lb, so a scope and a full magazine adding 0.81 lb would do it. Recoil velocity at that weight is 10.47 fps.
A muzzle brake works on the powder gas, and SAAMI notes its formula leaves brakes and suppressors out. The Brake or Suppressor Energy Cut field adds them back as a percentage. Enter the reduction the maker publishes for your device and caliber.
A 40% cut takes the loaded example from 16.51 to 9.908 ft-lbf. Recoil velocity falls to 8.927 fps and impulse to 2.220 lbf·s. The hero line keeps the bare-muzzle figure beside the new one, and Load B, the weight card and the table all take the same cut.
The Powder Gas Share row shows how much a brake has to work with. It is 34.9% for the rifle example and 7.8% for the 12 gauge load. Turning all of that gas sideways would cut recoil energy by 57.7% on the rifle but only 15.0% on the shotgun.
The result note warns when the cut you type is above that ceiling for your load. A 40% cut on the 12 gauge load is more than its gas can give, so it would need rear-angled ports. The figures are still worked out with the cut you entered.
Does a heavier bullet mean more recoil? Usually, but velocity and charge travel with it. Load B in the tool is a 180 gr bullet at 2,600 fps over 44 gr. It makes 17.70 ft-lbf, so the 150 gr load is only 6.71% lighter on the shoulder.
Low recoil is better for accuracy as long as the load still does its job downrange. Recoil builds over a session, and a flinch costs more hits than a slower muzzle velocity does.
Recoil Energy of a Nucleus
The same momentum rule gives the recoil energy of a nucleus formula in physics courses. A nucleus that emits a gamma photon recoils with the photon’s momentum, and the energy it takes follows from that.
$$E_R = \frac{E_\gamma^2}{2 M c^2}$$
For the 14.4 keV gamma ray of iron-57, with a rest energy near 53,000 MeV, the recoil is about 0.002 eV. The Recoil Energy Calculator above works in grains and pounds for firearms and does not include this nuclear case.
Recoil Questions Shooters Ask
How does recoil work, and why is it called recoil?
The powder gas pushes the bullet forward and pushes the gun back with the same force for the same time. That is Newton’s third law, and it leaves the gun and the ejecta with equal and opposite momentum. The word comes from the Old French reculer, to move backward.
What are the three types of recoil?
Recoil momentum builds in three stages. The bullet accelerates down the barrel, the powder gas accelerates behind it, and the gas then jets out of the muzzle once the bullet is clear. The SAAMI gas factor rolls the second and third stages into one powder gas velocity.
Why does gun recoil go up?
The barrel sits above the point where your shoulder or hand resists the gun. The recoil force pushes straight back along the bore, above that support, so the gun pivots and the muzzle climbs. A lower bore line or a straighter stock leaves less leverage for it.
Which guns have the highest and the least recoil?
Heavy payloads in light guns sit at the top. Chuck Hawks lists a 10 gauge 3.5 inch load with 2 1/4 oz of shot in a 10.5 lb gun at 62.9 ft-lbf. At the other end, a 40 gr rimfire bullet at 1,200 fps from a 6 lb rifle is about 0.12 ft-lbf before its small powder charge is counted.
What does zero recoil mean, and can a gun have it?
Zero recoil means no net momentum reaches the gun. A firearm that sends a bullet and gas forward cannot get there, because that momentum has to be balanced. Weight, a brake or a lighter load only shrink it. Recoilless weapons manage it by venting gas out the back.
How is recoil measured?
Free recoil is normally calculated, not measured, since the four inputs of a rifle recoil energy calculator are easy to weigh or chronograph. Energy is given in ft-lbf or joules, velocity in fps or m/s, and impulse in lbf·s or N·s. More energy tools sit in the Energy, Work and Power Calculators hub.