FPE Calculator

FPE Calculator finds foot-pounds and joules from pellet weight and chronograph fps, works FPE back to FPS or pellet weight, and checks the shot against a 12 ft-lb or 6 ft-lb limit.

How the FPE Calculator Rates an Airgun

The FPE Calculator turns a pellet weight and a chronograph reading into foot-pounds of energy, the number airgunners use to rate power. It also works backward, from a known FPE to the velocity a pellet should reach or the pellet weight that matches a target energy.

The menu at the top has three jobs. FPE from Weight and FPS is the usual one. FPS from FPE and Weight answers the FPE to FPS question, such as how fast a 12 ft-lb rifle should push a given pellet. Pellet Weight from FPE finds the weight that gives a chosen energy at a measured speed.

Pellet weight can be typed in grains or grams, and velocity in feet per second or meters per second. The default shot is an 8.44 grain .177 pellet at 780 fps. The FPE Calculator shows 11.4 ft-lb for it, which is 15.46 joules.

Open the Limit and Options panel to set a power limit, a second pellet weight to compare and the air temperature. The result cards then show how close the shot sits to the limit, what a heavier or lighter pellet would do, and how far the pellet is from the speed of sound.

The same panel has a Shot String box for a whole chronograph session. Type 2 to 50 readings separated by commas or spaces, and the FPE Calculator fills the velocity box with their average, so every result runs on the average shot rather than one reading.

FPE Formula for Pellets

Foot-pounds of energy is the pellet’s kinetic energy written in US units. Airgun makers, magazines and chronograph makers all use the same short formula, with weight in grains and velocity in feet per second.

$$FPE = \frac{w \times v^2}{450240}$$

w is the pellet weight in grains and v is the velocity in fps. The divisor 450,240 is 2 × 7,000 × 32.16, which folds in the one half from the kinetic energy formula, the 7,000 grains in a pound and a rounded value of gravity in ft/s².

For the default shot, 780 squared is 608,400. Multiply by 8.44 to get 5,134,896, then divide by 450,240 to get 11.40 ft-lb. The step list under the results prints these lines with your own numbers.

The Bullet Energy Calculator uses exact standard gravity, which gives a divisor of 450,436.686 instead. For this shot it returns 11.40 ft-lb as well. The two divisors differ by only 0.04 percent, far less than the shot-to-shot spread of any air rifle.

FPE to FPS Calculator

Turn the formula around and it gives the velocity a pellet needs for a set energy. This is the form used to check whether a rifle is shooting as it should.

$$v = \sqrt{\frac{FPE \times 450240}{w}}$$

A rifle set to the UK 12 ft-lb limit would push the 8.44 grain pellet at 800 fps. The same rifle would send a 10.34 grain pellet at 723 fps. If your chronograph reads well below these, the rifle is delivering less energy than its rating, often from a worn seal or a low fill.

FPS to Foot-Pounds Calculator

The forward direction is the one most shooters need after a chronograph session. Enter the weight on the pellet tin and the average speed you measured, and the hero figure is the muzzle energy in foot-pounds.

A .22 pellet of 16 grains at 580 fps makes 16 × 580² ÷ 450,240 = 11.95 ft-lb. That is almost the same energy as the .177 example, even though the .22 is 200 fps slower, because it is nearly twice as heavy.

FPE in Joules and Metric Units

Outside the US, airgun energy is usually quoted in joules. One foot-pound equals 1.355818 joules in the NIST conversion tables, so 12 ft-lb is 16.27 J and 6 ft-lb is 8.13 J.

To use the FPE Calculator as a muzzle energy calculator in metric, switch the weight to grams and the velocity to m/s, then pick joules as the result unit. The first result card of the FPE Calculator always shows the energy, speed and weight in the other system, so a metric and an imperial reading can be checked against each other.

In pure SI units the formula is E = ½mv², with m in kilograms and v in m/s. The default pellet weighs 0.5469 g and leaves at 237.7 m/s, which gives 15.46 J. A grain is exactly 64.79891 milligrams, which is how the tool moves between the two weight units.

The 12 ft-lb and 6 ft-lb Limits

Many airgunners run an FPE calculator to check a legal limit. In Great Britain, the Firearms (Dangerous Air Weapons) Rules 1969 declare an air weapon specially dangerous if the pellet leaves the muzzle with more than 6 ft-lb from an air pistol, or more than 12 ft-lb from any other air weapon.

That moves the gun out of the ordinary air weapon category and into firearms law. The British Pest Control Association puts it simply for its members, saying that air rifles with a muzzle energy over 12 foot pounds are classed as firearms.

The power limit field in the FPE Calculator starts at 12 ft-lb. Type 6 for a pistol, or any figure in joules if your local rule is written that way. The second result card then shows your margin, the velocity at which this pellet would sit exactly on the limit, and the pellet weight that would do the same at your measured speed.

For the default shot, the margin is 0.595 ft-lb, the limit velocity is 800.1 fps and the limit weight is 8.88 grains. A rifle close to the line can cross it with a heavier pellet in a spring gun or a higher regulator setting in a PCP, so the check is worth repeating after any change.

Airgun FPE Chart

This airgun FPE chart turns the question around. Each cell is the velocity in fps a pellet of that weight must reach to make the energy at the top of the column. Read across your pellet’s row to see where the common power levels fall.

The chart shows why light pellets suit low-power guns and heavy pellets suit high-power ones. A 7 grain pellet already needs 879 fps for 12 ft-lb, and at 20 ft-lb it would be past the speed of sound. A 25.4 grain pellet reaches 30 ft-lb at only 729 fps.

The FPE Chart block under the results gives the matching table for your own pellet. At airgun speeds it lists the energy in ft-lb and joules every 100 fps from 400 to 1,200 fps, with your own shot marked in its row.

Heavier Pellets and Velocity

A heavier pellet always leaves slower, but the energy it carries depends on the power plant. The third result card in the FPE Calculator estimates the change by assuming the gun delivers the same energy to both pellets. That is close for many regulated PCP rifles and only a rough guide for springers.

With the default settings, moving from 8.44 grains to 10.34 grains drops the speed from 780 fps to 704.7 fps, a loss of 75.3 fps. Momentum rises by 10.7 percent, because momentum grows with the square root of weight when the energy is fixed.

Real tests show the effect. In a Shooting UK test of JSB Exact Heavy pellets, Chris Wheeler weighed the 10.34 grain pellets at an average of 10.35 grains and recorded around 11.6 ft-lb from his rifle. Put those two numbers in the FPS mode and the tool gives a velocity of about 710 fps.

A spring-piston gun stores its shot energy in a compressed mainspring, which the Elastic Potential Energy Calculator can estimate from the spring rate and preload. Only part of that energy reaches the pellet, and heavier pellets often take a slightly larger share.

Staying Below the Speed of Sound

Diabolo pellets are shaped for subsonic flight. Tom Gaylord, writing as B.B. Pelletier for Pyramyd AIR, explains that pellets start to buffet in the transonic region below the sound barrier, which shows up as larger groups. He notes that many airgunners keep velocities under 900 fps for that reason.

The fourth result card of the FPE Calculator divides your velocity by the speed of sound at the air temperature you set. At the default 59 °F, sound travels at 1,116 fps, so the 780 fps shot is Mach 0.70 and 336.5 fps below the sound barrier. Colder air lowers the speed of sound and narrows that gap.

Gaylord’s 2021 update adds that some pellets can break the barrier and still group well, so treat the Mach figure as a warning sign, not a hard rule. A sharp crack beyond the normal muzzle report is the usual sign that a pellet has gone supersonic.

Using FPE at the Range

How do I measure pellet velocity?

Set a chronograph a short distance in front of the muzzle, as the maker’s instructions describe, and fire a string of shots. Paste all the readings into the Shot String box rather than picking one, because a single fast shot overstates the rifle’s power and a single slow one understates it.

The sample string of 776, 781, 779, 784 and 780 fps averages 780 fps. The Shot String table lists each shot with its energy, from 11.29 ft-lb for the slowest to 11.52 ft-lb for the fastest. It then gives an extreme spread of 8 fps and a standard deviation of 2.9 fps.

Extreme spread is the gap between the fastest and slowest shot, and standard deviation shows how tightly the rest cluster around the average. Low figures mean steady power, which keeps the point of impact steady at range. The tool divides by n − 1 for standard deviation, so a chronograph that divides by n can show a slightly lower figure, 2.6 fps for this string.

For a legal limit check, look at the energy of the fastest shot in the table as well as the average. A rifle whose average sits just under 12 ft-lb can still put single shots over it.

The Muzzle Velocity Calculator can estimate speed from energy and weight or from a timed distance if you have no chronograph. A chronograph reading is still the figure to trust for a legal limit check.

Can the FPE calculator be used for bullets?

Yes. The FPE formula is the same for any projectile, so an FPE calculator for bullets only needs the bullet weight in grains and the velocity in fps. A 40 grain .22 LR bullet at 1,200 fps makes 128 ft-lb, well beyond any pellet in the chart above.

The power limit and Mach cards are built around airguns, though. For firearms, the Bullet Energy Calculator adds the energy left at range from a G1 ballistic coefficient, along with power factor and momentum.

How much FPE does an air rifle need for pest control?

There is no single energy figure in UK law or guidance for humane pest control with an air rifle. The British Pest Control Association stresses that a humane shot relies on precision first, then on choosing a suitable pellet, and that you should only shoot at ranges where every pellet lands in the vital area.

The same guidance names .22 as suited to rabbits, squirrels and pigeons at sensible distances, since it delivers more momentum than .177. Many trained technicians are comfortable out to 20 to 30 metres. The third result card helps here, because it shows how much momentum a heavier pellet adds at the same energy.

Is there an FPE calculator app?

The FPE Calculator runs in a phone browser with nothing to install, so it serves as an airgun power calculator app at the range. The math runs on your device, and the inputs stack one per row on a small screen.

Copy Results puts the energy, speed and limit check on the clipboard, and Print Results saves them as a page or PDF. Both are handy when you keep a log of each rifle’s power after a service or a regulator change.

Energy, work and power tools for other jobs sit on the energy, work and power calculators hub, and the Ballistic Coefficient Calculator includes a GA pellet model for the downrange side of airgun shooting.