Bullet Energy Calculator gives muzzle energy in ft-lbf or joules from bullet weight and velocity, with energy left at any yardage, the half-energy range, power factor and momentum.
Enter the bullet weight and the muzzle velocity from the ammo box or a chronograph.
Distance, BC and Result Unit
Step-by-Step Working
- Known values: m = 168 gr, v = 2,650 fps, G1 ballistic coefficient = 0.462, distance = 100 yd
- Grain and fps shortcut: E = m × v² ÷ 450,436.686 = 168 × 2,650² ÷ 450,436.686 = 2,619.19 ft-lbf
- Convert to SI units: m = 0.0108862 kg, v = 807.72 m/s
- Kinetic energy: E = ½ × m × v² = 0.5 × 0.0108862 kg × (807.72 m/s)² = 3,551.15 J
- In foot-pounds: 3,551.15 J ÷ 1.35582 = 2,619.19 ft-lbf
- Velocity at 100 yd: G1 drag curve stepped every 0.5 m in standard sea-level air = 749.738 m/s
- Energy at 100 yd: 0.5 × 0.0108862 kg × (749.738 m/s)² = 3,059.61 J = 2,256.65 ft-lbf
- Power factor: 168 gr × 2,650 fps ÷ 1,000 = 445.2
Bullet Energy by Distance
| Distance (yd) | fps | ft-lbf |
|---|---|---|
| Muzzle | 2,650 | 2,619 |
| 100 | 2,460 | 2,257 |
| 200 | 2,277 | 1,935 |
| 300 | 2,103 | 1,649 |
| 400 | 1,936 | 1,398 |
| 500 | 1,778 | 1,179 |
What the Bullet Energy Calculator Works Out
The Bullet Energy Calculator needs two numbers to give a muzzle energy. One is the bullet weight, printed on the ammo box in grains. The other is the muzzle velocity, taken from the box or from your own chronograph.
Weight can be entered in grains, grams or ounces, and velocity in feet per second or meters per second. The large figure at the top is the muzzle energy in foot-pounds, written ft-lbf and often called ft-lbs. A switch in the options panel changes it to joules.
The default entry is a 168 grain bullet at 2,650 fps, a common .308 Winchester match load. The Bullet Energy Calculator returns 2,619 ft-lbf for it, which is the muzzle energy Federal prints for that load.
Open the panel under the main fields to add a distance and a G1 ballistic coefficient. The result cards then show the energy left at that range, the velocity there, the flight time and the distance where half the energy is gone. A fourth card lists power factor and momentum.
If you only know the energy and want the speed back, the Muzzle Velocity Calculator runs the same formula in reverse. Other energy tools sit on the energy, work and power calculators hub.
Bullet Energy Formula and the Physics Behind It
A bullet carries no explosive, so all the work it can do comes from its motion. Physics calls that kinetic energy, and it depends on mass and on the square of speed.
$$E = \frac{1}{2} m v^2$$
With mass in kilograms and velocity in meters per second, the answer is in joules. Shooters in the US work in grains and feet per second, so the same formula is usually written with the unit conversions folded into one divisor.
$$E = \frac{w \times v^2}{450436.686}$$
Here w is the bullet weight in grains, v is the velocity in fps and E comes out in foot-pounds. The divisor is built from three numbers that each have a plain meaning.
$$2 \times 7000 \times 32.174049 = 450436.686$$
The 2 is the one half in the kinetic energy formula. The 7,000 is the number of grains in a pound. The 32.174049 is standard gravity in ft/s², which turns pounds of mass into the pounds of force that a foot-pound is built on. Standard gravity is fixed at 9.80665 m/s² in the NIST conversion tables, and dividing by 0.3048 gives the value in feet.
A 9mm load makes a quick check of the bullet energy formula. Take a 124 grain bullet leaving the barrel at 1,150 fps, square the velocity, multiply by the weight and divide.
$$E = \frac{124 \times 1150^2}{450436.686} = 364.07$$
That is 364 ft-lbf of muzzle energy. The step list under the result cards in the Bullet Energy Calculator prints this same line with your own numbers, followed by the SI working, so you can copy it into a load log.
Why Some Sources Divide by 450,240
Many loading manuals and older calculators use 450,240 as the divisor. That number is 2 × 7,000 × 32.16, where 32.16 ft/s² is an older, rounded value for gravity.
The two divisors differ by 0.044 percent. For the 168 grain load above, 450,240 gives 2,620 ft-lbf and 450,436.686 gives 2,619 ft-lbf. For the 9mm load the gap is 364.23 against 364.07.
A difference of one foot-pound never changes a decision about a load. It does explain why two tools can disagree in the last digit when you enter the same weight and velocity.
Bullet Energy in Joules
Ammunition sold outside the US often lists energy in joules, and some range and hunting rules are written in joules too. One foot-pound equals 1.355818 joules, so multiply ft-lbf by that factor to convert.
The 168 grain load at 2,619 ft-lbf carries 3,551 J. The 9mm load at 364 ft-lbf carries 494 J. The first result card in the Bullet Energy Calculator always shows the energy in whichever unit you did not pick as the main one.
If the box gives weight in grams and velocity in m/s, there is a metric shortcut that skips grains entirely. It is the kinetic energy formula with the grams-to-kilograms step built in.
$$E = \frac{m \times v^2}{2000}$$
With m in grams and v in m/s, E is in joules. The same .308 bullet weighs 10.89 g and leaves at 807.7 m/s, and 10.89 × 807.7² ÷ 2,000 again gives 3,551 J. One grain is exactly 64.79891 milligrams, which is the factor the calculator uses to move between the two systems.
Bullet Energy Over Distance
Muzzle energy only describes the first instant of flight. Air drag slows the bullet from then on, and because energy follows the square of velocity, it drops faster than speed does.
To work out bullet energy over distance, the Bullet Energy Calculator needs a G1 ballistic coefficient. Makers print it on the box or the product page, and a higher number means the bullet holds its speed better. If you have two chronograph readings instead, the Ballistic Coefficient Calculator will find the BC from them.
The calculator steps the bullet along the G1 drag curve every half meter and reads off the velocity at your range. The table below sets its output beside the figures Federal publishes for its 168 grain Gold Medal .308 load, which has a BC of 0.462 and was tested in a 24 inch barrel.
| Distance | Federal velocity | Calculator velocity | Federal energy | Calculator energy |
|---|---|---|---|---|
| Muzzle | 2,650 fps | 2,650 fps | 2,619 ft-lbf | 2,619 ft-lbf |
| 100 yd | 2,460 fps | 2,460 fps | 2,257 ft-lbf | 2,257 ft-lbf |
| 200 yd | 2,277 fps | 2,277 fps | 1,935 ft-lbf | 1,935 ft-lbf |
| 300 yd | 2,103 fps | 2,103 fps | 1,650 ft-lbf | 1,649 ft-lbf |
| 400 yd | 1,936 fps | 1,936 fps | 1,398 ft-lbf | 1,398 ft-lbf |
| 500 yd | 1,778 fps | 1,778 fps | 1,179 ft-lbf | 1,179 ft-lbf |
By 500 yards this bullet has lost 33 percent of its velocity and 55 percent of its energy. Half the muzzle energy is gone at 439 yards, and the bullet stays supersonic out to about 1,060 yards. The third result card reports both of those distances for any load.
All downrange figures assume the sea-level standard that US ballistics tables are built on, which is 59 °F, 29.53 inHg and 78 percent humidity. Thinner air at altitude or on a hot day means less drag, so real energy at range runs a little higher there. Lilja Precision Rifle Barrels gives an example where a 0.265 BC behaves like 0.330 at about 5,300 feet.
Bullet Energy Chart by Weight and Velocity
A bullet energy chart is useful when you want a rough figure without typing anything. Each cell below is the energy in ft-lbf for that weight and speed, from the same 450,436.686 formula.
| Bullet weight | 1,000 fps | 1,500 fps | 2,000 fps | 2,500 fps | 3,000 fps |
|---|---|---|---|---|---|
| 40 gr | 89 | 200 | 355 | 555 | 799 |
| 55 gr | 122 | 275 | 488 | 763 | 1,099 |
| 115 gr | 255 | 574 | 1,021 | 1,596 | 2,298 |
| 124 gr | 275 | 619 | 1,101 | 1,721 | 2,478 |
| 150 gr | 333 | 749 | 1,332 | 2,081 | 2,997 |
| 168 gr | 373 | 839 | 1,492 | 2,331 | 3,357 |
| 180 gr | 400 | 899 | 1,598 | 2,498 | 3,597 |
| 230 gr | 511 | 1,149 | 2,042 | 3,191 | 4,596 |
The chart is pure arithmetic, so some cells are speeds no real cartridge reaches with that bullet. Read across a row and the pattern is clear. Going from 1,000 to 2,000 fps multiplies the energy by four, and going to 3,000 fps multiplies it by nine.
A handy rule falls out of the 1,000 fps column. At that speed every grain of bullet carries 2.22 ft-lbf. For speeds or weights between the rows, the Bullet Energy Calculator gives the exact figure and draws its own energy curve for your load.
Bullet Weight or Velocity: Which Adds More?
Velocity is squared in the formula and weight is not. Raise the velocity of the 168 grain load by 10 percent, to 2,915 fps, and the energy climbs 21 percent to 3,169 ft-lbf. Raise the weight by 10 percent instead and the energy climbs only 10 percent, to 2,881 ft-lbf.
That is why a light, fast bullet can match a heavy, slow one on paper. A 124 grain 9mm bullet at 1,150 fps has 364 ft-lbf. A 230 grain .45 bullet at 850 fps has 369 ft-lbf. The two are almost equal in energy.
They are not equal in momentum. The 9mm load carries 20.4 lb·ft/s and the .45 load carries 27.9 lb·ft/s, about 37 percent more. Momentum is the quantity that felt recoil follows, and the Momentum Calculator covers it on its own.
Practical pistol matches rank loads by momentum through a figure called power factor. It uses the same two inputs as energy, but velocity is not squared.
$$PF = \frac{w \times v}{1000}$$
Weight is in grains and velocity in fps. The 9mm load above scores 142.6 and the .45 load scores 195.5. Under the USPSA competition rules a load needs 125 to count as Minor and 165 to count as Major, so these two loads land in different classes despite near-identical energy. That is why the Bullet Energy Calculator shows power factor next to momentum on its fourth card.
Energy Minimums for Deer and Elk
Hunters use a ft-lbs muzzle energy calculator mostly to answer one question, which is whether a load still has enough energy at the range of the shot. Some states write a number into law. Colorado requires a rifle for elk to be at least .24 caliber, with an expanding bullet of at least 85 grains that delivers 1,000 ft-lbf at 100 yards.
The same Colorado Parks and Wildlife ballistics lesson treats 1,000 ft-lbf as enough for deer. For elk it quotes a general consensus of 1,200 ft-lbf for a broadside shot and at least 2,000 ft-lbf for a quartering shot.
To find where your load crosses a threshold, change the distance in the Bullet Energy Calculator until the second result card shows that energy. The 168 grain example falls to 2,000 ft-lbf at about 179 yards, to 1,500 ft-lbf at 358 yards, to 1,200 ft-lbf at 490 yards and to 1,000 ft-lbf at 595 yards.
Energy is a floor to clear and tells you nothing about how the bullet behaves in the animal. The Colorado lesson notes that standard bullets keep 45 to 55 percent of their weight after impact, while controlled expansion bullets keep 70 to 85 percent. The example load above uses a match bullet, so its numbers show the method only. Check your own state’s regulations for the legal minimum.
Bullet Energy Questions
How do you calculate bullet energy at 100 yards?
Use the same formula with the velocity the bullet has at 100 yards instead of the muzzle velocity. For the 168 grain .308 load, the speed at 100 yards is 2,460 fps, and 168 × 2,460² ÷ 450,436.686 gives 2,257 ft-lbf.
The hard part is knowing that downrange velocity. You can read it from the maker’s ballistics table, measure it with a chronograph set at the target, or let the calculator work it out from the muzzle velocity and the G1 BC.
Does barrel length change bullet energy?
Yes, because it changes muzzle velocity. Factory figures come from a test barrel, which was 24 inches for the Federal load in the table above. A shorter barrel gives the powder gas less time to push, so the bullet leaves slower.
The loss in energy is larger than the loss in speed. A bullet that leaves 5 percent slower than the box figure has 9.75 percent less muzzle energy. A chronograph reading from your own rifle or pistol is the most reliable velocity to enter.
Is muzzle energy the same as stopping power?
No. Muzzle energy is a physical quantity you can calculate exactly from weight and velocity. Stopping power has no agreed definition and no unit, and it depends on where the bullet hits and how it expands or penetrates.
Two loads with the same energy can act very differently in a target. The 9mm and .45 loads compared earlier are within 5 ft-lbf of each other, yet they differ in diameter, in weight and in momentum. Energy is best used to compare similar bullets, or to check a load against a stated minimum.
Can I use it for airgun pellets, slugs and arrows?
The muzzle energy figure works for any projectile, since the formula only needs a weight and a speed. A 14.3 grain airgun pellet at 800 fps has 20.3 ft-lbf. A one ounce shotgun slug weighs 437.5 grains, and at 1,600 fps it carries 2,487 ft-lbf. The weight field accepts ounces directly.
The downrange cards assume a G1 ballistic coefficient, which suits most bullets but not every pellet or slug shape. Arrows are usually worked from the bow’s rating, and the Arrow Speed Calculator gives arrow velocity and kinetic energy from draw length and arrow weight.
Is there a bullet energy calculator app?
Phone apps exist, but none is needed for this job. The Bullet Energy Calculator runs in a phone browser with one field per row, and the math is done on your device, so the weight and velocity you type are not sent anywhere.
At the range, enter the average of your chronograph string as the muzzle velocity. Open the options panel if you want the energy at your target distance, and switch the result unit to joules if your club’s limit is written that way.