Enter the following five values and click the Calculate button:

Examples to Try

6.5 Creedmoor: 6.2 lbs rifle, 147 gr bullet,
39 gr powder, 2600 fps, 0% muzzle brake

.700 Nitro Express Dangerous Game Rifle: 18 lbs rifle, 1000 gr bullet,
160 gr powder, 2000 fps, 0%
muzzle brake

6.5 Creedmoor AR10 Rifle: 8.5 lbs, 147 gr bullet, 39 gr powder, 2560
fps, 0% muzzle brake

Barret Model 82A1 50BMG Rifle: 32.7 lbs, 655 gr bullet, 248 gr powder,
3029 fps, 90% muzzle brake

US Army M4 5.56 Rifle & M193 ball ammo: 6.5 lbs, 56 gr bullet,
27.5 gr powder, 3250 fps, 10% muzzle brake (flash hider)

22LR rifle: 6 lbs, 40 gr bullet, 2.5 gr powder, 1185 fps, 0%
muzzle brake

12 gauge shotgun: 7 lbs, firing 2 3/4 inch shot shell with 1 3/8 ounces
of shot (multiply ounces by 437.5 to convert to grains, so 601.6 grains + 20
grain wad = 621.6), 35.5 gr powder at 1310 fps, 0% muzzle brake

Glock 17 full size 9mm pistol: 2 lbs (fully loaded), 115 gr bullet, 6
gr powder, 1050 fps, 0% muzzle brake

S&W Model 340 PD Airlight 357 Mag Revolver: 0.74 lb, 158 gr bullet, 13
gr powder, 1115 fps, 0% muzzle brake

Same S&W Model 340 PD Airlight 357 Mag Revolver shooting
38 Special: 158 gr bullet, 4.5 gr powder, 640 fps, 0% muzzle brake

S&W Model 686 Plus 357 Mag Revolver: 2.3 lbs, 158 gr bullet,
13 gr powder, 1115 fps (same load as the Airlight above)

S&W Model 500 8 inch 50S&W Revolver: 4.46 lbs, 700 gr bullet, 27.5 gr
powder, 1300 fps, 40% muzzle brake

Same S&W 500 with 275 gr bullet
with 40 gr powder, 1804 fps

308 Win Rifle is the default gun, just refresh your browser to load
the .308 rifle numbers

When I began studying weapon recoil I was surprised to find most of
the mathematical theory was from the early 1900's. The formulas from
these early texts are still in common use today but they do not jive
with current muzzle brake research.
Classic recoil formulas greatly underestimate the recoil generated by
the exit gas from the muzzle or the "jet effect".
Like uncorking champaign, when a bullet clears the muzzle, gas
accelerates and shoots past the bullet. This acceleration of gas out
of the muzzle is called the "jet effect" and accounts for approximately
10 to 55% of total recoil energy.

PrecisionRifleBlog.com did an excellent series of articles on muzzle brake
effectiveness. The graphs below from these articles show how much force is
generated by the jet effect.

The top blue graph line is recoil force without a muzzle
brake. Notice how recoil levels off at 420 pounds when the bullet exits the
muzzle. After bullet exit the force jumps to 655 pounds as exit gas blows out of
the muzzle. This shows that for the 6XC cartridge in this gun, approximately
36% of recoil force is from the exit gas jet effect [(655-420) / 655 = .36].
This chart is from the
PrecisionRifleBlog.com muzzle brake test article with annotations added by
me.

The reduction in recoil highlighted in magenta above is due
to a combination of the muzzle brake weight and muzzle brake exit gas
redirection.

Arms and Explosives
(1909, page 20) used a constant velocity of 3200 feet-per-second for gas
muzzle exit velocity. I believe this "constant" is wholly antiquated
when used with today's high efficiency smokeless gun powders. Instead of
using a constant I have found a more accurate estimate of muzzle gas
velocity is bullet muzzle velocity * 1.7. Adding this to the classic
formula brings calculated recoil much closer to modern recoil
measurements and muzzle brake tests. You can see in this super slow
motion film gas shoots past the bullet exiting the muzzle. This
acceleration out of the muzzle causes jet effect recoil.

Super Slow Motion Bullet Muzzle Exit

Note how much faster the gasses exiting the muzzle are
compared to the bullet.

Gun recoil momentum and energy are generated
in three ways:

1. The
acceleration of the bullet in the barrel.

Bullet Momentum is equal to: Bullet
Weight * Muzzle Velocity

Bullet Energy is equal to: Bullet
Weight * Muzzle Velocity squared / 2g [g is the acceleration of gravity
feet-per-second per-second and is equal to 32.17405]

An equal and opposite reaction to the
bullet acceleration is transferred to the gun.

2. The
acceleration of the powder burn gasses inside the barrel.

Gas Momentum is equal to: Powder
Weight * Muzzle Velocity / 2

We use the powder weight because the
gas created when the powder burns is equal to the powder weight.

An equal and opposite reaction to the
gas acceleration is transferred to the gun.

We divide the muzzle velocity
by 2 because as the bullet moves from breech to muzzle, the powder's
center of gravity only moves from the breech to the center of the barrel
when the bullet exits the muzzle.

3. The "jet
effect" of the powder burn gasses exiting the muzzle.

Jet Effect Momentum is approximately
equal to: Powder Weight * Muzzle Velocity * 1.7

When a muzzle brake is used Jet Effect Momentum = Powder Weight * Muzzle
Velocity * 1.7 * (1 – Muzzle Brake Efficiency)^(1/√℮)

Gas exit velocity is estimated at:
1.7 * bullet muzzle velocity

An equal and opposite reaction to the
jet effect is transferred to the gun.

When a bullet clears the muzzle, gas
accelerates and shoots past the bullet. This force is what a muzzle brake acts
upon. A brake's additional weight will also reduce recoil energy (but the
additional weight does not affect gun recoil momentum).

Jet Effect Momentum Formula

GasExitVelocity = MuzzleVelocity * 1.7

Gun Recoil Momentum, Impulse, Velocity and Energy

Also

Gun Recoil Impulse Formula

g = acceleration of gravity feet-per-second
per-second = 32.17405

g = acceleration of gravity feet-per-second
per-second = 32.17405, 2g = 64.35

The above equations assume all powder is burned inside the
barrel. A slow burning powder that doesn't completely burn inside the barrel can
greatly reduce bullet velocity and recoil
because unburned powder imparts no energy to the bullet and has no jet effect. I
use
QuickLOAD, an internal ballistics
program, to select powders that will burn completely in a given barrel length.

Gun & Optic g Force tells us how hard our scope
will be hit during recoil. The g force calculated is what the
firearm would feel if shot while hanging from strings (free recoil). When we shoulder
a rifle or hold a pistol some of our body weight is added to the
effective gun weight so the more securely we hold a firearm the less g force
the gun and optic will actually feel. We calculate the recoil velocity
of the gun and divide it by the time the bullet is accelerating inside
the barrel which gives us acceleration in feet-per-second. We then
divide that acceleration by g to get the number of g's the
rifle and optic experience.

When calculating GunVelocity I leave out JetEffectMomentum
and just use BulletMomentum + GasMomentum.
I do this because the
highest recoil g force will come during bullet acceleration and
we can calculate exactly how much time the bullet is in the barrel so we
can ignore what happens after the bullet leaves the barrel.

Bullet Acceleration Inside Barrel

The blue line shows bullet speed in fps (right scale)
inside a 22" 6.5 Creedmoor barrel. The bullet reaches 50% of muzzle velocity after only
2.6 inches of travel. The slope of the blue line corresponds to acceleration.
The steeper the slope, the quicker the acceleration and the higher the g. The
graph was created using QuickLOAD internal
ballistics software.

We can calculate precisely how long the bullet is in the
barrel by dividing BarrelLength by the average speed of the bullet in
the barrel. I subtract 1 inch from barrel length because manufacturer
barrel length includes the chamber. The barrel length is then converted
to feet and MuzzleVelocity is in feet-per-second. Bullets initially accelerate very
fast in the barrel so their average speed through the barrel is about 60% of MuzzleVelocity.

After dividing GunVelocity by BarrelTime we divide the
resulting acceleration by g, which is the acceleration of
gravity. The value of g is a constant equal to 32.17405 feet-per-second
per-second. The result is the number of g's the gun and optic
experience when hanging from strings and fired but will be lower when
fired from the shoulder or held securely in the hands. The more firmly a firearm is held the lower the g felt by the firearm and
optic. If we clamp a firearm into a large vise and fire it the gun and
optic will feel no acceleration and no g. My old F-15 Eagle
fighter could keep me at 9g for a couple of minutes but optics routinely
take over 500g's when bolted to a light and powerful gun.

A heavier gun will give us slightly higher muzzle
velocity.

Work is calculated by multiplying force by the distance over
which that force is applied. Consider this thought experiment: The gun and
bullet both weigh 1 pound. This formula says the loss of velocity to gun weight
= 1 / (1+1) = 0.5 so 50% of the energy from the expanding propellant gas is used
to propel the gun and 50% propels the bullet. If the gun were placed against an
immovable wall the gun weight is equivalent to infinity and loss of velocity to
gun weight = 0 so all the energy of the propellant is used to push the bullet
and muzzle velocity doubles. There are 7000 grains in a pound so for an 8 pound
rifle firing a 200 grain bullet the formula is: loss of velocity = 200 / (8*7000
+ 200) = 0.4% loss, so 99.6% of the
work done by the expanding gas is applied to the bullet and 0.4% to the
rifle.

Now let's look at a very light pistol, the 0.74 lb S&W 340 PD
Airlight 357 Magnum, firing a 200 grain bullet: 200 / (0.74 * 7000 + 200) = 3.7%
loss so even at the extreme, gun weight has little effect on muzzle velocity. If
muzzle velocity is 800 fps with the pistol clamped down then we'd lose only 30
fps to 770 fps when fired hanging from strings (free recoil). A firm, strong grip on the
pistol will cut that velocity loss because it increases the effective weight of
the pistol.

All other things being equal, a lighter gun will have more recoil energy. The Smith & Wesson Model 340 PD 357 Mag revolver
with a 2 inch barrel and made of Scandium and Titanium is extremely light at
0.74 lb. It kicks like a mule when firing heavy 357 Mag bullets. Plug in these
numbers in the recoil calculator above: 158 gr bullet, 13 gr of powder, 0.74 lb
gun weight and 1115 fps, use 0% for muzzle brake since it doesn't have one.
That gives us a very stout 18.6 ft-lbs of recoil energy from this "Airlight"
pistol. Fire the same exact load from the S&W Model 686 Plus, which weighs 2.3
lbs, and the recoil energy drops to a very manageable 6.0 ft-lbs, a 68%
reduction in recoil energy due solely to the extra pistol weight!

S&W's 357 Magnum Airlight pistols are so light their recoil energy
noticeably increases as you empty the gun. Four 158gr 357 Magnum cartridges
weigh approximately 0.12 lbs (the 340 PD holds five rounds but one is being
fired in this example). For the first shot the pistol + 4 cartridges weigh
0.74 + 0.12 = 0.86 lb which gives us 16.0 ft-lbs of recoil energy compared to
the last shot at 18.6 ft-lbs for a 16% increase in recoil energy!

The 8 inch barreled S&W 500 50 caliber pistol weighs in at 4.46 lbs and fires
a 700 gr bullet at 1300 fps using 27.5 gr of powder. I estimate its barrel ports
at 40% efficient as a muzzle brake. Plug those numbers into the calculator above
and we get an amazing 67 ft-lbs of recoil energy! The same exact pistol firing a
275 gr bullet with 40 gr of powder will give us 1804 fps of muzzle velocity
with a recoil energy of "just" 28 ft-lbs.

The US Army's M4 rifle using M193 ball ammunition comes in at 6.5
lbs, 56 gr bullet at 3050 fps using 27.5 gr of powder and a 10% efficient
muzzle brake (flash hider) with a paltry 5.9 ft-lbs of recoil energy.

A 6 lb .22 rifle using a 22LR cartridge: 40 gr bullet, 2.5 gr
powder at 1185 fps, no muzzle brake, hits us with 0.17 lb of recoil
energy!

When I fire my 20 lb Serbu BFG-50 50BMG rifle with a typical 50
cal round, 655 gr bullet, 248 gr powder at 3029 fps, with the muzzle
brake removed it generates a whooping 210 ft-lbs of recoil energy.
That's why it has a big muzzle brake. Assuming the muzzle brake weighs 1
lb and is 90% efficient, the recoil energy drops to 114 ft-lbs (46% less
recoil) which is still a serious kick in the shoulder.

A 7 lb 12 gauge shotgun firing 2 3/4 inch shot shell with 1 3/8 ounces of shot
(multiply ounces by 437.5 to convert to grains, so 601.6 grains + 20 grain wad =
621.6), 35.5 gr powder at 1310 fps and no muzzle brake gives us 38 ft-lbs or
recoil energy.

I added a pair of these
XLR Industries M-LOC Steel Chassis Weights to my Tikka T3x TAC A1 and
6.5mm Ruger Precision Rifle. Adding a pair at 15 total ounces will reduce
the Tikka and 6.5 Creedmoor
Ruger Precision Rifle's recoil energy by 8%. The 6.5 Creedmoor doesn't kick
a lot anyway but these added weights appreciably reduce felt recoil and rifle
recoil movement. Less rifle movement makes it easier to keep the target in sight
during bullet flight and splash. They're easy to remove if you want to take the
rifle hunting. If you want a dual-purpose long range rifle for hunting and
target shooting I recommend a carbon fiber wrapped barrel for light weight
hunting, then add one or two pair of these chassis weights for target shooting.

All other things being equal, a faster burning powder will
generate a "sharper" or "snappier" recoil with a higher peak energy.
This can be caused by two factors: more of the powder is burned in the
barrel generating more energy and the quicker we accelerate the bullet
in the barrel the shorter the recoil energy impulse.

Peak recoil energy plays a major part in our perception of recoil. The
more secure a gun is when it is fired, the higher the peak recoil energy. A gun
mounted in a vise will show a much higher peak energy compared to the same gun
fired from the shoulder when standing because the shoulder will move and spread
the recoil over a longer time period. The same recoil energy is absorbed by the
vice and shoulder but the time in which it is absorbed affects the energy peak.
This is why using a "lead sled" can crack a wooden stock and why modern
artillery has "shock absorbers" which allow the barrel to move in recoil.

The AR-15 bolt buffer works by spreading the bolt recoil impulse over time.
When the bolt strikes the buffer it transfers its recoil momentum to the buffer
then the buffer spring spreads the buffer recoil energy over time. The bolt
recoil energy isn't reduced but it is spread out so felt shoulder recoil isn't
as "sharp" and perceived recoil is reduced.

Pistols use much less powder than rifles therefore they generate less gas and
jet effect recoil. Less jet effect recoil means a muzzle brake or compensator
will have less effect.

All other things being equal, heavier pistol bullets strike high
due to more recoil & more muzzle jump.

A shorter barrel can result in higher muzzle pressure and therefore more
jet effect. A shorter barrel also reduces weight which also adds to gun recoil
velocity and recoil energy.

Jet effect recoil becomes more prominent with the use of high
velocity lightweight bullets. Lightweight bullets generate less
recoil but the jet effect is the same so it becomes a higher percentage
of total recoil energy.

A note about momentum versus energy: Momentum is
calculated by simply multiplying weight x velocity whereas energy is velocity
squared x weight / 2g [g is the acceleration of gravity feet-per-second
per-second and 2g is equal to 64.35 fps-ps]. Squaring velocity means energy is more
affected by velocity--the relationship between energy and velocity is nonlinear
so it's not quite as intuitive as momentum. If we double the velocity we don't
double the energy, it is quadrupled.

A 100 grain
bullet with a muzzle velocity of 1000 fps has a momentum of
14.3 and 222 ft-lbs of energy

A 100 grain
bullet with a muzzle velocity of 2000 fps has a momentum of
28.6 and 888 ft-lbs of energy

With double the velocity
the momentum doubles but the energy quadruples.
This is why lightweight but high velocity bullets do so much damage and
one of the reasons the US Army adopted the 5.56 cartridge for the M16.

Recoil Versus Bullet Weight

Bullet muzzle energy is equal to:

We can see from the formula that since muzzle velocity is
squared it will have more effect on energy than bullet weight.

Let's compare the recoil from two loads with the same muzzle
energy but different weight bullets fired from 7 lb rifles:

34 grain 22-250 bullet with 38 grains
of powder at 4500 fps muzzle velocity and 80% effective muzzle brake has 1529
ft-lbs of muzzle energy and hits the shooter with 5.5 ft-lbs of
recoil energy.

300 grain 338 Win Mag bullet with 40
grains of powder at 1515 muzzle velocity and 80% effective muzzle brake has the
same 1529 ft-lbs of muzzle energy but hits the shooter with 12.4
ft-lbs of recoil energy--125% more recoil than the 22-250!

The lighter and faster bullet causes much less recoil at the
same muzzle energy. This is why light weight, high velocity calibers are
popular with recoil sensitive shooters and is another reason the US Army
chose 5.56 for the M16 rifle.

Muzzle Brakes

Muzzle brakes are designed to reduce recoil force by redirecting exit gas and
minimizing the jet effect but their additional weight also reduces recoil
energy. Adding an 8oz (half pound) muzzle brake to a 6.2 pound 308 rifle reduces
its recoil energy by 7.4% due solely to the added weight. The best muzzle brake
in the PrecisionRifleBlog test was the Alamo Four Star (now called
MPA Cowl Induction Brake) weighs in at 6 oz and would reduce recoil energy
on the same rifle by 5.6% due to added weight.

All other things being equal, the lighter the gun, the higher the recoil
energy and the more effective a muzzle brake becomes.

Typically, the more powerful the gun, the more effective a muzzle brake
becomes. This is why all 50BMG rifles have large muzzle brakes.

Since muzzle brakes are designed to reduce jet effect recoil, pistol
muzzle brakes are less effective due to the small amount of gun powder (and
therefore gas) used in pistols. But their added weight can reduce recoil
significantly. Adding a half-pound muzzle brake to a 2 pound pistol will cut
recoil energy by 20% due solely to the added weight.

Surprisingly, the
PrecisionRifleBlog muzzle brake test found that
using the correct caliber muzzle brake isn't that important. Shooting 6mm through a
7.62mm muzzle brake was only 1 to 3% less effective in reducing recoil compared
to the same brake in 6mm.

“The Johnson muzzle brake. This reduces recoil from forty to fifty percent
by actual test”, Hatcher’s Notebook p269.
PrecisionRifleBlog.com muzzle brake tests
show a similar maximum recoil momentum reduction of 44%. Since recoil momentum
is not affected by weight we know all 44% of this recoil reduction is from
redirected exit gas.

The top blue graph line is recoil force without a muzzle
brake. Notice how recoil levels off at 420 pounds when the bullet exits the
muzzle. After bullet exit the force jumps to 655 pounds as exit gas blows out of
the muzzle. In this graph 36% of recoil energy is caused by the jet effect.
This graph is from the
PrecisionRifleBlog.com muzzle brake test article with annotations added by
me.

Even with a perfectly designed muzzle brake there will be exit gas that will
escape through the brake's bore hole. Even so, theoretically a muzzle brake can
be more than 100% efficient if it can send enough exit gas rearward to make up
for the gas that escapes through the bore hole. Any exit gas that turns more
than 90 degrees from the bore axis (rearward) will actually produce force
opposite the recoil (forward thrust).

Suppressors

A good suppressor or "silencer" is typically about 50% as effective in
reducing rifle recoil momentum compared to a good muzzle brake. Pistol
cartridges use relatively small amounts of powder and therefore generate less
jet effect gas than rifles so pistol suppressors have less gas to work with and
only reduce recoil by approximately 5 to 10%.

The added weight of a suppressor also reduces recoil. Since pistols are
light, the additional weight of a suppressor can greatly reduce their recoil.
The weight of a SilencerCO Osprey 45 ACP suppressor (0.65lb) installed on a
fully loaded Glock 21 (full size 45 ACP at 2.47lb) will cut recoil energy by 21%
due to the added suppressor weight. The same suppressor installed on a Glock 17
with empty magazine (full size 9mm at 1.55lb) will cut recoil energy by 30% due
to weight alone. Total suppressor recoil reduction from gas redirection and
added weight usually comes in around
25% for pistols and 15 to 40% for rifles.

A pistol suppressor also reduces muzzle flip by making the weapon longer
which spreads its weight over a greater length increasing its moment of inertia
thereby reducing rotation (muzzle flip is a rotational force).

A suppressed pistol with a red dot sight can be frighteningly accurate. Less
noise, less recoil, less muzzle flip and a sighting system that can take
advantage it.

Hot, burning, expanding gas explodes out of the barrel around the bullet.
This hot gas accelerating out of the muzzle imparts an equal and opposite force
to the pistol as "Jet Effect" recoil.

Note how the bullet is clear of the barrel and the slide has moved rearward
less than 1/10th of an inch.

Note how jet effect gas hits the base of the bullet and shoots outward at 90
degrees. This gas is moving much faster than the bullet and is on average 1.7
times faster than bullet muzzle velocity. Even after the bullet clears the
barrel gas continues to push the bullet for about 15 bullet diameters (calibers) downrange
which equals 6.75 inches with this 45 pistol. This is why
the shape of the bullet base or boat tail can have an effect on accuracy.

This flame outside the barrel represents gas expansion that did not occur in
the barrel and did not propel the bullet or generate gas recoil or jet effect
recoil. A faster burning powder would be more efficient.

Jet effect gasses continue to push the bullet until it gets approximately 15
bullet diameters (calibers) from the muzzle. For this .45 caliber we get: .45 *
15 = 6.75 inches.

9mm

Note how the bullet is clear of the barrel and the slide has moved rearward
less than 1/10th of an inch.

Compare this 9mm muzzle flame to the 45ACP above. This powder is burned
quickly and efficiently inside the barrel.

Another Video of Super Slow Motion Bullet Muzzle Exit

Be sure and watch the revolver shot at the end of the
video.

By Major Rob Robinette

US Army and Air Force (Retired)

Major Robinette was a Battalion Marksmanship Champion,
Squadron Rifle Team Captain and Range Officer. Rob also spent 10 years
as a federal law enforcement officer. He holds a Federal Firearms
License and is the owner of
Nolichucky Guns. He enjoys all forms of rifle and pistol use.