How this instrument works
Free recoil energy comes straight from conservation of momentum: the instant a bullet leaves the muzzle, whatever forward momentum it carries, the gun carries backward in equal measure. Set the two momenta equal — bullet mass times bullet velocity on one side, gun weight times recoil velocity on the other — and solve for the gun's velocity. The 7000 in the denominator is not a physics constant; it is the conversion between grains, the unit bullets are weighed in, and pounds, the unit guns are weighed in — 7000 grains to the pound, exactly, by definition.
The second step turns that recoil velocity into energy the way any moving mass does: one-half mass times velocity squared. Because gun weight is entered in pounds — a force, not a mass — the formula divides by standard gravity, 32.174 ft/s², to get the slug of mass the kinetic-energy equation actually needs. The result is free recoil: the energy the gun would carry if nothing stood in its way. A stock, a recoil pad, and the shooter's shoulder do not change this number; they only change how the same energy is spread out and felt, which is a separate problem in biomechanics, not momentum.
This version of the formula, the one on gun-shop ballistics charts and reloading manuals, counts only the bullet's momentum. SAAMI's full free-recoil standard adds a second term for the propellant gas leaving the muzzle, treating its velocity as roughly 1.75 times the bullet's velocity for rifles, which meaningfully raises the total for magnum loads carrying heavy powder charges. Gunsmiths sizing a stock, hunters choosing between two rifle weights, and reloaders comparing loads all use this simplified bullet-only figure, and the common mistake is assuming recoil tracks the bullet's muzzle energy — it does not; a light, fast bullet and a heavy, slow one can leave the muzzle with identical energy yet produce different recoil, because recoil depends on momentum, not energy, until this last step converts one into the other.
- Enter the bullet's weight in Bullet mass (grains) — read straight off the ammunition box or a reloading manual.
- Enter the muzzle speed in Bullet velocity (fps), the figure printed alongside bullet weight or measured with a chronograph.
- Enter the firearm's weight, scope and sling included, in Gun weight (lb).
- Read Recoil velocity (fps) — how fast the gun itself moves backward the instant the bullet leaves.
- Read Free recoil energy (ft-lb) — the energy delivered to the shoulder before any stock, pad, or brake absorbs it.
Worked example — a 150-grain load from an 8 lb rifle
Take a 150-grain bullet leaving the muzzle at 2,700 fps from an 8 lb rifle — a fairly typical deer-rifle load. Recoil velocity first: Vr = (150 × 2700) ⁄ (7000 × 8) = 405,000 ⁄ 56,000 = 7.232 fps. That is how fast the rifle itself accelerates backward in the instant of firing, before the shooter's shoulder, sling, or stock have any say in the matter.
Energy follows the same numbers: Er = 0.5 × 8 × 7.232² ⁄ 32.174 ≈ 6.50 ft-lb. That sits toward the mild end for a centerfire hunting rifle — noticeably less than a .300 Winchester Magnum's typical 25-plus ft-lb — and is a reasonable trade for the flatter trajectory the same cartridge gives downrange. Halve the gun weight to 4 lb with the identical load and recoil velocity doubles to 14.46 fps; because mass halves while velocity squared quadruples, the free recoil energy also exactly doubles, to about 13.0 ft-lb.
Questions
Why does 7000 appear in the recoil velocity formula?
Because bullets are weighed in grains and guns in pounds, and 7000 grains equal exactly one pound by definition. The formula uses that ratio to bring bullet mass into the same unit as gun weight before the momentum equation can balance. Rework the formula in grams and kilograms and the 7000 has to disappear entirely — it is a unit-conversion factor, not a physical constant, which trips up anyone trying to adapt it to metric inputs without redoing that step.
What is the difference between free recoil energy and felt recoil?
Free recoil energy, the number this instrument returns, is what the gun would carry if it flew backward completely unimpeded. Felt recoil is what actually reaches the shooter's shoulder, and it depends on stock shape and length of pull, a recoil pad's cushioning, a muzzle brake venting gas sideways, and even how tightly the gun is held. Two rifles with identical free recoil energy can feel very different in the hands, which is why free recoil is a starting point for comparison, not the last word.
Does this formula include the propellant gas, or just the bullet?
Just the bullet. SAAMI's full free-recoil standard adds a second momentum term for the propellant gas leaving the muzzle, modeling its velocity at roughly 1.75 times the bullet's velocity for rifles, which measurably increases total recoil for magnum loads carrying heavy powder charges. This simplified bullet-only formula is what appears on standard reloading and ballistics charts, because it only needs bullet weight, bullet velocity, and gun weight — numbers printed on any ammunition box.
Why does a heavier rifle recoil less than a lighter one firing the same cartridge?
Because the bullet leaves with a fixed amount of forward momentum, and conservation of momentum demands the gun absorb an equal amount going the other way. Spread that momentum over more mass and recoil velocity drops proportionally; spread it over less mass and velocity rises. Recoil energy falls even faster in a heavier gun, since it depends on velocity squared, which is exactly why hunters carrying stout cartridges often deliberately choose a heavier rifle.
Where does the 32.174 in the energy formula come from?
It is standard gravity, 32.174 ft/s², the US customary equivalent of the 9.80665 m/s² NIST lists in SI units. Gun weight is entered in pounds, a unit of force, not mass; dividing by standard gravity converts that weight into slugs, the mass unit the kinetic-energy formula — one-half mass times velocity squared — actually requires. Skipping this conversion is a common error in home-built recoil spreadsheets, and it inflates the energy figure by a factor of roughly 32.
Is 6.5 ft-lb of free recoil energy considered heavy?
No — it sits toward the mild end of centerfire rifle recoil. Shooters and gunwriters commonly treat figures under 15 ft-lb as comfortable for most people, 15 to 20 ft-lb as noticeable, and past 20 ft-lb as demanding real technique; light mountain rifles in big magnum chamberings can exceed 40 ft-lb. An 8 lb rifle shooting a 150-grain bullet at 2,700 fps, this page's own worked example, lands comfortably in the mild range at about 6.5 ft-lb.