Kinetic Energy Calculator for Archers — KE, Momentum, and What's Enough for the Animal
Kinetic energy is the number every hunter checks first. It's also the number that gets misused the most. KE alone does not kill an elk. KE plus momentum, the right broadhead, and FOC do. This page gives you the math, the minimums per game class, and the calculator that does it all.
The Forge bakes this into the Broadhead Confidence Score, which runs your build against 8 game classes and tells you HIGH, ADEQUATE, MARGINAL, or INSUFFICIENT.
What kinetic energy is
KE is the energy of motion. For archery, it's measured in foot-pounds (ft-lb) and it tells you how much work the arrow can do at impact. More KE means more potential to break ribs, drive a broadhead, and exit the offside.
It does not tell you the whole story. A light, fast arrow can carry the same KE as a heavy, slow one, but they don't penetrate the same. That's where momentum comes in. More on that below.
The KE formula
KE (ft-lb) = (Mass × Velocity²) / 450,240
Where mass is total arrow weight in grains and velocity is in feet per second. The 450,240 constant is the conversion factor that turns grains and fps into foot-pounds.
Example. 450-grain arrow at 285 fps:
KE = (450 × 285²) / 450,240 = (450 × 81,225) / 450,240 = 36,551,250 / 450,240 = 81.2 ft-lb.
That's plenty for any North American big game except moose and brown bear, where you want to push closer to 85.
The momentum formula
Momentum (slug-feet per second) = Mass × Velocity / 225,218
Same 450-grain arrow at 285 fps:
Momentum = (450 × 285) / 225,218 = 128,250 / 225,218 = 0.569 slug-ft/s.
Momentum is the better predictor of penetration on heavy game. Dr. Ed Ashby's two-decade penetration study at the Natal Game Ranch concluded that momentum, FOC, and mechanical advantage of the broadhead matter more than raw KE once you're past the threshold to break bone.
KE minimums by game class
These are the Easton-published recommendations, widely adopted as the industry baseline:
- Small game (rabbit, squirrel): under 25 ft-lb
- Medium game (turkey, javelina): 25 ft-lb
- Large game (whitetail, antelope, mule deer): 25-41 ft-lb
- Heavy game (elk, black bear, wild boar): 42-65 ft-lb
- Toughest game (moose, grizzly, cape buffalo): 65+ ft-lb
These are minimums to consider an ethical shot, not targets. Most modern compound bows produce 70-90 ft-lb at the riser with a well-built arrow. The minimums are floors. The Forge's Broadhead Confidence Score grades you against the floor and against a recommended margin above it.
Why both numbers matter
Consider two builds at 75 ft-lb of KE.
Build A: 380-grain arrow at 297 fps. KE = 74.5 ft-lb. Momentum = 0.501.
Build B: 525-grain arrow at 254 fps. KE = 75.2 ft-lb. Momentum = 0.592.
Same KE. Build B has 18% more momentum. On a Wyoming bull elk at 35 yards, both will likely kill cleanly. On a quartering shot through the ball joint into the offside vitals, Build B punches through and exits. Build A might stop in the cavity. That's the Ashby finding in one sentence.
If you hunt anything heavier than whitetail, build for momentum first. The KE number will come along for the ride.
How The Forge does it
Punch in your arrow (or use a saved build from the Arrow Builder), drop your chronograph velocity, and The Forge returns KE, momentum, drop, drift, and the Broadhead Confidence Score across all 8 game classes. The Confidence Score weighs KE, momentum, FOC, and broadhead type, then maps each game class to a band:
- HIGH — well above the threshold, full confidence
- ADEQUATE — meets recommended values
- MARGINAL — at the floor, take your shot carefully
- INSUFFICIENT — do not take this animal with this setup
It's calibrated against Easton's published minimums, the Ashby penetration work, and the 2025 Yates broadhead study.
Open The Forge. Hunter tier ($6/mo) unlocks the full Broadhead Confidence Score. Free tier gives you KE and momentum on any saved build.
FAQ
How much kinetic energy do I need for elk?
Easton's published minimum is 42 ft-lb. We recommend 55+ for a comfortable margin, with momentum above 0.55 slug-ft/s. Most modern 65-pound compounds with a 460-grain arrow at 280 fps hit that easily.
Is KE or momentum more important?
KE for soft tissue. Momentum for bone and penetration. On heavy game, momentum is the better predictor. On whitetail, either works.
What's a good KE for whitetail?
25-40 ft-lb meets the published minimum. Most hunters land in the 60-80 ft-lb range with a modern compound, which is comfortable margin. A 425-grain arrow at 280 fps is 74 ft-lb.
Does arrow weight matter more than speed for KE?
Speed matters more in the equation because it's squared. But heavier arrows retain energy better downrange and carry more momentum. The optimal build trades a bit of speed for mass.
How do I measure my actual arrow velocity?
Chronograph. A Caldwell G2 or LabRadar Lite at the shop or your own backyard. Manufacturer IBO speeds are useless for KE math because they assume a 5-grain-per-pound arrow at 30-inch draw, which is not your setup.
Will a 50-pound bow produce enough KE for deer?
Yes. A 50-pound compound with a 400-grain arrow at 240 fps produces 51 ft-lb. That's well above the whitetail threshold. The legal minimum in most states is 35-40 pounds of draw weight.