Formula
Momentum of the free gun equals momentum of the ejecta plus the powder gas. SAAMI takes the gas weight as the powder charge, because the gas is hard to weigh, and sets gas velocity to a factor times muzzle velocity. That factor is 1.75 for a high-powered rifle, 1.50 for a pistol, revolver, or average shotgun, and 1.25 for a long shotgun barrel. Those factors are from the 1929 British Text Book of Small Arms, as SAAMI’s sheet records them. Recoil speed is that momentum divided by 7,000 times the gun weight in pounds. Free recoil energy is the gun weight times speed squared, divided by 64.34. Impulse is gun weight times speed, divided by 32.17. SAAMI uses 32.17 ft/s², so twice that is 64.34 rather than 64.348.
Vf = (WE × VE + WPC × VE × f) / (7,000 × WF)
FRE = WF × Vf² / 64.34
A heavier gun lowers the speed and the energy for the same ejecta. A muzzle brake, a suppressor’s gas path, a pad, and the action are outside the formula. Felt recoil is not this number. The powder figure is one you already have from a published source. This page does not choose it and does not print a pressure. Muzzle energy of the ejecta uses the same grains × velocity squared ÷ 450,437 identity as the bullet energy page.
Worked examples
Rifle, 150 gr at 2,800 ft/s, 46 gr powder, 8 lb, f = 1.75. Recoil speed 11.525 ft/s. Energy 16.515 ft·lb, about 22.39 J. Impulse 2.866 lbf·s. The same load in a 10 lb rifle is 9.220 ft/s and 13.212 ft·lb.
Charge left blank. 7.5 ft/s and 6.994 ft·lb, marked incomplete. SAAMI’s average shotgun: 7 lb, 589.9 gr ejecta, 33.4 gr powder, 1,275 ft/s, f = 1.50, about 16.653 ft/s and 30.17 ft·lb. Pistol example: 115 gr at 1,150 ft/s, 5 gr powder, 1.5 lb, f = 1.50, about 13.417 ft/s and 4.20 ft·lb.
Reference
1 ounce is 437.5 grains. 1 ft·lb is 1.355818 J. These examples are arithmetic checks, not loads to assemble or fire.
Questions
How do you calculate free recoil energy?
SAAMI equates powder-gas weight to the charge, sets gas velocity to a factor times muzzle velocity, then treats the gun’s rearward speed as momentum over 7,000 times gun weight. Energy is gun weight times that speed squared, divided by 64.34.
What is free recoil versus felt recoil?
Free recoil is the firearm moving as a free body. Felt recoil changes with the pad, the stock, the action, and anything that redirects gas. This page is only the free-body number.
Does a muzzle brake change this number?
Not unless you change the inputs yourself. SAAMI’s sheet says the formula ignores gas redirected by a brake or a suppressor. The gun’s weight still includes those parts if they are on it.
How much does the powder charge affect recoil?
It is the gas term. The rifle example with 46 grains is 16.5 ft·lb. The same bullet with the charge left blank, so the gas term is omitted, is about 7.0 ft·lb, and the page marks that figure incomplete.
Why do rifle and shotgun use different factors?
SAAMI’s sheet, from the 1929 British Text Book of Small Arms, uses 1.75 for a high-powered rifle, 1.50 for a pistol or an average shotgun, and 1.25 for a long shotgun barrel. You can type another factor.
Is this the same formula as SAAMI?
Yes. Velocity is (ejecta × velocity + charge × velocity × factor) / (7,000 × gun weight). Energy uses 64.34, which is twice 32.17. SAAMI’s own shotgun example prints about 30 ft·lb; full precision here is 30.17.
Can I compare two loads?
Yes. A second gun weight is optional. The rifle example is 16.5 ft·lb at 8 pounds and 13.2 ft·lb at 10 pounds. That comparison is not a suggestion to fire either one.
Sources
- SAAMI, Gun Recoil Formulae, revised 9 July 2018. Free recoil from conservation of momentum. Gas weight equals the powder charge. VPG = f × VE, with f = 1.75, 1.50, or 1.25 as listed. Those factors are credited to the 1929 British Text Book of Small Arms. Energy uses g = 32.17 ft/s², so the divisor is 64.34. The sheet’s shotgun example is about 30 ft·lb; full precision on those inputs is 30.17.
- SAAMI notes that brakes and suppressors, which redirect gas, and pads or action type, which change how fast the force arrives, are outside free recoil. Firearm weight includes attachments.
- Muzzle energy reuses this site’s bullet-energy identity, grains × ft/s squared ÷ 450,437. No powder table is printed here.