Muzzle Velocity Calculator finds bullet speed at the muzzle from muzzle energy and bullet weight, a timed distance or barrel pressure. It also shows muzzle energy, Mach and recoil.
Enter the muzzle energy and the bullet weight printed on the ammunition box.
Gun Weight and Units
Step-by-Step Working
- Known values: E = 2,800 ft·lbf (3,796.3 J), m = 150 gr (9.72 g)
- Rearrange E = ½mv²: v = √(2 × 3,796.3 ÷ 0.00971984) = 883.82 m/s
- Convert to feet per second: 883.82 ÷ 0.3048 = 2,899.7 ft/s
- Common shortcut: 150 gr × (2,899.7 ft/s)² ÷ 450,240 = 2,801.2 ft·lbf, about 0.04% high because it rounds gravity
- Result: 2,899.7 ft/s (883.82 m/s) with 2,800 ft·lbf (3,796.3 J)
Energy at Other Velocities
| Velocity | Muzzle Energy | Compared |
|---|---|---|
| 2,319.7 ft/s | 1,792 ft·lbf | −36% energy |
| 2,609.7 ft/s | 2,268 ft·lbf | −19% energy |
| 2,899.7 ft/s | 2,800 ft·lbf | Your result |
| 3,189.6 ft/s | 3,388 ft·lbf | +21% energy |
| 3,479.6 ft/s | 4,032 ft·lbf | +44% energy |
Energy-Velocity Graph
Muzzle Velocity Calculator Methods
Muzzle velocity is the speed of a bullet at the moment it leaves the barrel. It is called that because the muzzle is the open front end of the barrel. The bullet is at its fastest there, and air drag slows it from that point on.
The Muzzle Velocity Calculator reaches the number four ways, set under Calculate From. Energy and Bullet Weight works back from the figures printed on an ammunition box. Velocity and Bullet Weight runs the other way and gives muzzle energy. Distance and Time uses a timed gap, and Barrel Pressure and Length gives an ideal estimate.
The default is a 150 gr bullet with 2,800 ft·lbf of muzzle energy, which comes to 2,899.7 ft/s. The cards convert that to 883.82 m/s and Mach 2.58. They also give the momentum, the power factor, the recoil velocity of the gun, and the time and drop over 100 yards.
Muzzle Velocity Formula
The muzzle velocity formula comes from kinetic energy. Energy equals half the mass times the velocity squared, so the velocity is the square root of twice the energy divided by the mass. This is the form taught in physics classes, with energy in joules and mass in kilograms.
$$v = \sqrt{\frac{2 E}{m}}$$
The formula for calculating muzzle energy is the same line turned around. For shooting units there is a shortcut, with bullet weight w in grains, velocity in feet per second and energy in foot-pounds.
$$E = \frac{w \times v^2}{450437}$$
Many charts use 450,240 as the divisor, which rounds gravity to 32.16 ft/s². The difference is 0.04%. A 150 gr bullet at 2,900 ft/s has 2,800.6 ft·lbf with the exact constant, and the Muzzle Velocity Calculator shows both versions in its working.
The two numbers describe different things. Muzzle velocity is a speed. Muzzle energy is the work the bullet can do, and it depends on the bullet weight as well. Raising the velocity by 10% raises the energy by 21%, because the velocity is squared.
Measuring Muzzle Velocity
The device used to measure muzzle velocity is a chronograph. An optical chronograph has two light sensors a known distance apart and times the bullet between them. A radar chronograph tracks the bullet with Doppler radar and needs nothing placed in front of the gun.
The Distance and Time setting of the Muzzle Velocity Calculator does the sum an optical unit does. A bullet that takes 3.45 ms to cross a 10 ft gap is moving at 2,898.6 ft/s. This is the average speed between the sensors, so it sits slightly under the true value at the muzzle.
Anyone asking how to know their own muzzle velocity has two honest options. The number on the ammunition box is the maker’s figure from a test barrel. A chronograph gives the figure for one particular gun, which often differs because of barrel length.
Without a Chronograph
The simplest way to calculate muzzle velocity without a chronograph is from published energy. Enter the muzzle energy and the bullet weight from the box, and the first setting of the Muzzle Velocity Calculator returns the velocity the maker measured.
The Barrel Pressure and Length setting is a physics estimate. It multiplies an average pressure by the bore area to get a force, and the force by the barrel length to get the work done on the bullet. With 20,000 psi average pressure on a .308 in bore and a 150 gr bullet, the ideal figures by barrel length are below.
| Barrel length | Ideal muzzle velocity |
|---|---|
| 16 in | 2,442.6 ft/s |
| 20 in | 2,730.9 ft/s |
| 24 in | 2,991.6 ft/s |
These are upper estimates. Real pressure peaks early and falls as the bullet moves, and friction takes a share. The average pressure is far below the peak chamber pressure quoted for a cartridge, so entering the peak figure gives a velocity that is much too high.
Textbook problems often use a third route, the recoil of the gun. Momentum is conserved, so the bullet’s mass times its velocity equals the gun’s mass times its recoil velocity. A 3 kg rifle recoiling at 2 m/s from a 10 g bullet means the bullet left at 600 m/s. The Conservation of Momentum Calculator handles that kind of problem.
Muzzle Velocity of Common Rounds
The table runs published loads through the Muzzle Velocity Calculator. The .22 LR figures are from CCI, whose Standard Velocity load is listed at 1,070 ft/s and 102 ft·lbf. The 9 mm row is a 115 gr practice load listed at 1,180 ft/s, and the rifle row is the example the tool opens with.
| Load | Muzzle velocity | In m/s | Mach | Muzzle energy |
|---|---|---|---|---|
| .22 LR, 40 gr, quiet load | 710 ft/s | 216.41 | 0.63 | 44.8 ft·lbf |
| .22 LR, 40 gr, standard velocity | 1,070 ft/s | 326.14 | 0.95 | 101.7 ft·lbf |
| .22 LR, 40 gr, high velocity | 1,235 ft/s | 376.43 | 1.1 | 135.4 ft·lbf |
| 9 mm, 115 gr | 1,180 ft/s | 359.66 | 1.05 | 355.5 ft·lbf |
| Rifle, 150 gr | 2,900 ft/s | 883.92 | 2.58 | 2,800.6 ft·lbf |
| .220 Swift, 48 gr | 4,100 ft/s | 1,249.7 | 3.64 | 1,791.3 ft·lbf |
So the muzzle velocity of a .22 rifle with standard .22 LR ammunition is about 1,070 ft/s, just under the speed of sound. High-velocity loads reach 1,235 ft/s. A .22 is not stronger than a 9 mm. The 9 mm load carries about 3.5 times the energy of the standard .22 LR load.
The muzzle velocity of the AK-47 is about 700 m/s according to Britannica. That is 2,297 ft/s, 2,520 km/h or Mach 2.04. Centerfire rifles commonly run from around that figure to a little over 3,000 ft/s.
A speed of 3,000 ft/s is fast for a bullet. It equals 914.4 m/s, 2,045 mph and Mach 2.67. The highest velocities come from light bullets in large cases. The .220 Swift of 1935 was the first factory cartridge to pass 4,000 ft/s.
Ft Lbs for Air Rifles
Airgun power is quoted in foot-pounds, and the same formula applies. In the Muzzle Velocity Calculator, choose Velocity and Bullet Weight and enter the pellet weight in grains. An 8.44 gr pellet at 800 ft/s has 11.99 ft·lbf. A 14.3 gr pellet at 620 ft/s has 12.2 ft·lbf, and an 18.13 gr pellet at 870 ft/s has 30.47 ft·lbf.
Working backward is just as common. For a 12 ft·lbf air rifle, an 8.44 gr pellet leaves at 800.3 ft/s and a 14.3 gr pellet at 614.8 ft/s. The heavier pellet is slower at the same energy, which is why a chronograph reading means little without the pellet weight.
Is Higher Muzzle Velocity Better?
Higher velocity gives a flatter path and less time for wind to act. At 2,899.7 ft/s a bullet covers 100 yards in 0.1035 s and drops 2.07 in over that distance before drag is counted. How quickly it loses that speed depends on its shape, which the Ballistic Coefficient Calculator covers.
Lower velocity has its uses too. A subsonic bullet makes no sonic crack, and a slower bullet of the same weight produces less recoil. With the default load and a 7.5 lb gun, the bullet alone gives a recoil velocity of 8.28 ft/s and 8 ft·lbf of recoil energy. Powder gas adds to both.
The second card of the Muzzle Velocity Calculator lists momentum and power factor, which is bullet weight in grains times velocity in ft/s divided by 1,000. The default load scores 434.95. Momentum for any projectile can be worked separately in the Momentum Calculator, and sight corrections for the drop are converted in the MOA Calculator.