Momentum vs Kinetic Energy in Archery: Why the Arrow With 4% More Energy Carries 19% Less Momentum
A 350-grain arrow at 320 fps carries 4% more kinetic energy than a 550-grain arrow at 250 fps. It also carries 19% less momentum. Put both in front of the same gel block with a bone plate behind it and, in my model, the light one stalls while the heavy one exits. I ran the numbers, drew the impact diagrams, and built four free tools underneath so you can check your own arrow.
Core Insight: Kinetic energy (KE = ½·m·v²) measures the work an arrow can do. Momentum (p = m·v) measures how hard the arrow is to stop. Speed counts twice in energy and once in momentum, so light, fast arrows top the energy chart and heavy, slower arrows top the momentum chart. For penetration, and above all for bone, I rank momentum first and energy second.
Ideal for: whitetail and medium game
About 0.55 to 0.58 slug·ft/s covers it. A 450 gr arrow near 280 fps lands there and still shoots flat.
Ideal for: elk, bear, big bone
0.56 is the floor and 0.60 to 0.65 gives real margin on a shoulder. Think 550 gr and up.
Ideal for: anyone proud of a chronograph number
Check momentum before you celebrate speed. The calculator below takes ten seconds.
| Criteria | Kinetic energy | Momentum |
|---|---|---|
| What it measures | Work the arrow can do on whatever stops it | The push the arrow carries forward |
| Formula (grains, fps) | grains × fps² ÷ 450,240 ft·lb | grains × fps ÷ 225,218 slug·ft/s |
| Speed weighting | Squared: 10% more speed is 21% more energy | Linear: 10% more speed is 10% more momentum |
| Strongest at ranking | Soft-tissue work, comparing bows, target butts | Bone, heavy hide, shafts that survive the hit |
| Weak point | Can rank a light arrow above a heavy one that goes deeper | Says nothing about broadhead sharpness or alignment |
| Check it first if you hunt | Deer-class game, soft-tissue shots only | Elk, bear, anything with shoulder or ribs in play |
Both numbers come from the same two inputs. They differ in what each one predicts well.
What Is the Difference Between Kinetic Energy and Momentum in Archery?
Kinetic energy is the work an arrow can do on whatever stops it. Momentum is mass times speed: the shove the arrow can deliver, and the reason a heavy arrow is hard to knock off line.
Both numbers use the same two inputs, weight and speed. They disagree about how much each one deserves. Energy squares the speed, so a fast arrow gets rewarded twice. Momentum gives speed one vote and mass one vote.
How do you calculate arrow kinetic energy?
450,240 = 2 × 7,000 grains per pound × 32.16 ft/s². It turns grains into slugs and supplies the ½ from ½·m·v².
Take the 350 gr arrow at 320 fps: 350 × 320² ÷ 450,240 = 79.6 ft·lb. That equals a 10 lb bowling ball dropped from about 8 feet. Stop the arrow over 9.6 inches and it pushes back with roughly 100 lb, averaged over the stop. The work-energy theorem is the physics behind that last line.
How do you calculate arrow momentum?
225,218 = 7,000 grains per pound × 32.174 ft/s². Some shop charts round the constant to 225,400; the gap is under 0.1% and never flips a ranking. Multiply by 4.448 to get kg·m/s.
Same arrow: 350 × 320 ÷ 225,218 = 0.497 slug·ft/s (2.21 kg·m/s). Stop it in 5 milliseconds and the average force is p ÷ t, about 99 lb. Same arrow, same stop, same force as the energy math gave. When resistance stays constant, both views agree. The impulse-momentum relationship covers that side.
Why do the two rankings disagree?
A bow trades speed for mass. Hold the energy fixed and momentum becomes p = √(2·m·KE). Heavier arrows carry more momentum from the same energy, but only by the square root of their mass. Doubling the weight buys 41%, not 100%.
| Arrow weight | Speed for 60 ft·lb | Kinetic energy | Momentum (slug·ft/s) |
|---|---|---|---|
| 300 gr | 300 fps | 60.0 ft·lb | 0.400 |
| 400 gr | 260 fps | 60.0 ft·lb | 0.462 |
| 500 gr | 232 fps | 60.0 ft·lb | 0.516 |
| 600 gr | 212 fps | 60.0 ft·lb | 0.565 |
Energy is pinned at 60 ft·lb; only the mass-speed split changes. Momentum climbs 41% from the lightest to the heaviest row.
Enter your current arrow and speed, then drag the test weight. Speed for the new weight follows the same virtual-mass rule as the Arrow Speed & Performance Calculator, so a heavier arrow gives up less speed than the old grains-per-fps rule of thumb claims.
Model: v = vyours × √((wyours + 30) ÷ (w + 30)), one fixed bow. Energy flattens out while momentum keeps climbing. The five-build table further down uses typical real-world speeds instead of one bow, so its heavy entries lose a little more speed than this rule does.
How Do a Light Fast Arrow and a Heavy Slow Arrow Behave in Gel and Bone?
Terminal ballistics is what happens once the broadhead touches the target: how deep the arrow travels, what it has to cut through, and whether it exits.
Below, the same comparison as a diagram. One gel block, one bone plate behind it, two arrows. The loop is stylized, since arrows cut instead of blasting a cavity, but the outcomes match how the benchmark table ranks them.
A · 350 gr @ 320 fps
- 79.6 ft·lb and 0.497 slug·ft/s
- Crosses the gel first, reaches the bone with less push than B
- Editorial bone score 4.0 of 10: stalls on the plate
B · 550 gr @ 250 fps
- 76.3 ft·lb and 0.611 slug·ft/s
- Loses the energy race by 4%, wins the push race by 23%
- Editorial bone score 9.2 of 10: splits the plate and exits
Which number predicts penetration depth: energy or momentum?
Physics gives an “it depends”, and the dependency has a number on it. If tissue pushes back with a constant force, depth equals energy divided by that force and the light arrow wins by 4%. If the resistance grows with speed, the push has to be spent over time, momentum sets depth, and the heavy arrow wins by 23%.
Real tissue sits somewhere between. The widget below lets you dial the speed-dependent share of resistance and shows where the winner flips.
Resistance is modeled as F(v) = F0 + c·v. Slide the speed-dependent share and read the relative depth of each arrow, with arrow A set to 100.
0% means constant resistance (a pure work-energy problem). 100% means resistance proportional to speed (a pure momentum problem). Share is measured at 300 fps. This is a two-parameter sketch of tissue, not a tissue simulator. The Pass-Through Calculator and the simulator below price depth in proportion to momentum, which is this slider’s 100% end, so they rank arrows by momentum alone.
I would not call energy irrelevant. Under a constant cutting force it sets depth, and the widget agrees. But a real arrow leaks energy into shaft flex, blade deployment, wobble in bone and drag through hair and hide, and most of those leaks grow with speed. That tilts the field toward the heavy arrow.
The momentum-first penetration argument goes further and claims tissue resistance rises with the square of speed. Treat that as his claim, not a settled law. Soft-tissue-only shot? The energy camp is fine. Bone in the path? I take momentum every time.
Where does FOC fit in?
FOC (front of center) is how far the arrow’s balance point sits ahead of the shaft’s midpoint, as a percentage of arrow length.
Front weight keeps the shaft tracking straight behind the head, so the head keeps cutting instead of yawing when it meets bone. Easton lists 10 to 15% FOC for hunting setups. Penetration builds usually run 12 to 18%. Extreme-FOC builds beyond roughly 19% are debated, and I treat them as a specialist choice.
In the calculators below, FOC moves modeled depth by about 1.2% per point above 12%, capped at +20%. Measure yours with the Arrow FOC & Balance Point Optimizer.
Why do single-bevel broadheads rotate, and does the twist help in bone?
A single-bevel broadhead has one flat face and one angled face on each blade, so tissue pushes harder on one side than the other.
Tissue pushes on the angled face at a right angle to it. That push splits into a small part along the shaft, which slows the arrow, and a big part sideways, which twists the tip. For a bevel about 13° off the axis that is 0.23 along and 0.97 across.
The Ashby Foundation credits single-bevel heads with splitting bone through rotational force, and arrow builders on trad forums repeat that account. The mechanics do not settle the question. The twist costs a sliver of forward push and it loads the shaft, so the shaft has to be built for it.
My read: the twist earns its keep on elk-class game and larger, where bone is the whole problem. On whitetail it is a preference, not a requirement. For the fixed-versus-mechanical side of the head decision, see Mechanical vs Fixed Broadheads.
What Do Five Common Arrow Builds Look Like on Paper?
Specific momentum is arrow momentum divided by the bow’s draw weight. I show it ×1,000 at a 70 lb reference draw, which tells you how much of the bow’s effort goes into push instead of speed.
Five representative builds, from a target-and-small-game arrow to a big-bone build. Watch how flat the energy column stays: 73 to 80 ft·lb across all five. Momentum climbs 31%, and the editorial bone score climbs nearly 2.5 times.
| Build | Arrow | KE (ft·lb) | Momentum (slug·ft/s) | Specific momentum | Bone score (1–10) | Typical fit |
|---|---|---|---|---|---|---|
| Ultra-Light Speed | 350 gr @ 320 fps | 79.6 | 0.497 | 7.1 | 4.0 | Target, small game |
| Light Hunting | 400 gr @ 298 fps | 78.9 | 0.529 | 7.6 | 5.5 | Pronghorn, light deer |
| Balanced Hunting | 450 gr @ 280 fps | 78.4 | 0.559 | 8.0 | 7.2 | Whitetail, mule deer |
| Heavy Penetrator | 550 gr @ 250 fps | 76.3 | 0.611 | 8.7 | 9.2 | Elk, black bear |
| Dangerous Game | 650 gr @ 225 fps | 73.1 | 0.649 | 9.3 | 9.9 | Buffalo, big-bone game |
Representative builds with typical real-world speeds, not one bow. Specific momentum is ×10−3 slug·ft/s per pound at a 70 lb draw. Bone score is an editorial 1–10 planning rating for breaching a shoulder-blade-class bone plate. I set it by hand from the physics above and the field reports, no calculator here produces it, and it is not lab data.
What is the specific-momentum sweet spot?
| Specific momentum | Band | What it favors |
|---|---|---|
| Below 7.3 | Speed-tilted | Flat trajectory, thin bone margin |
| 7.3 to 8.4 | Balanced | Deer-class, livable trajectory |
| 8.4 to 9.0 | Penetration-tilted | Elk-class, angled shots |
| 9.0 and up | Heavy-game tilt | Buffalo-class bone |
If I had one do-everything hunting arrow, I would sit at the top of the balanced band, around 8.0 to 8.4. Past that point the trajectory penalty starts costing more than the extra bone margin returns, unless bone is the plan.
Which Free Tools Check Your Own Arrow?
Two more tools follow. The first turns any weight and speed into energy, momentum and a class rating. The second estimates pass-through odds using the same model as the Kinetic Energy, Momentum & Pass-Through Calculator.
Type your numbers or tap a preset build. The badges show what an energy-only rating says next to what a momentum rating says. When they disagree, trust the lower one for bone.
Class bands: energy thresholds follow the site’s other calculators (42 ft·lb deer-class, 65 ft·lb elk-class). Momentum bands sit halfway between the benchmark builds above. The Pass-Through Calculator uses a soft-tissue model with no bone and is more lenient: with a fixed head at 12% FOC, about 0.39 reaches elk vitals and about 0.61 passes through. These bands add margin for bone, angles and imperfect hits. Planning guides, not legal or lab standards.
Pick an arrow, a head and an animal. The gauges show the chance that modeled depth clears the vitals and the far side, using the shared ArcheryEra penetration model with a 22% scatter in tissue resistance. There is no bone in this model, so read it as a soft-tissue check and use the momentum floors above for bone.
Probability is the share of shots where modeled depth beats the target depth when tissue resistance varies by 22% (one standard deviation). A ranking aid, not a prediction for any single shot. Single bevel uses the cut-on-contact multiplier and does not model bone-splitting rotation.
Which Arrow Setup Fits Your Game?
Match the arrow to the hardest thing it might hit, not the softest. Momentum targets below come from the same weight-and-speed pairs as the benchmark table; FOC ranges follow the earlier section. Check your state’s minimum draw weight and energy rules first, since some states write kinetic energy into the regulation (draw weight and kinetic energy for deer).
| Game and use | Arrow weight | Speed target | Momentum | FOC | Broadhead direction |
|---|---|---|---|---|---|
| Small game & target | 350–400 gr | 298–320 fps | 0.50–0.53 | 8–12% | Fixed cut-on-contact, or blunts for small game |
| Whitetail & medium game | 450 gr | about 280 fps | about 0.56 | 10–14% | Fixed 3-blade, or a mechanical you have proven flies true |
| Elk, moose & large game | 550 gr | about 250 fps | about 0.61 | 12–16% | Fixed cut-on-contact; single bevel if bone is the plan |
| Dangerous & big-bone game | 650 gr and up | about 225 fps | 0.65 and up | 15–19% | Single bevel on a shaft built for the torque |
Weight and speed are pairs that fit typical hunting bows, not promises for any one bow. Run yours through the tools above.
- Where the forums land: threads such as penetration: is it KE or momentum, Kinetic Energy vs. Momentum and the long-running TradTalk thread The momentum myth re-run the same argument in both directions. This is my editorial read, not a poll.
- Top praised feature: heavy, high-FOC arrows that keep working on angled and bone-adjacent hits, including on trad bows where speed is limited.
- Common friction point: nobody agrees on how much speed is worth giving up, and the trajectory penalty past 30 yards is the complaint that keeps returning.
- Where the pragmatists end up: choose weight for the biggest game you hunt, check both numbers, then spend the rest of the effort on broadhead alignment and FOC. Outdoor Life’s physics-for-bowhunters piece makes the case against energy-only thinking in mainstream terms.
- Avoid if your shots are inside 25 yards, your bow tops out near 45 lb and the target is whitetail. A 650 gr arrow buys a rainbow trajectory with no bone to justify it.
- Avoid if the shaft spine is not matched to the added weight. A weak, heavy arrow bends in bone and gives back everything you paid for in mass.
- Avoid if you drop below your bow maker’s minimum arrow weight. Very light arrows can overload the limbs.
Our Final Take: Energy tells you what your bow is doing. Momentum tells you what your arrow will do when it meets something hard. Use energy to compare bows and momentum to choose arrows.
👉 Recommendation: for whitetail-class game, a 450 gr arrow near 280 fps with 10 to 14% FOC is the balance point. If elk or bone-heavy shots are on your list, step to 550 gr and 12 to 16% FOC before you chase another 10 fps. Then confirm the head flies like your field points with the Broadhead Flight Tuning & Stability Checker.
What Is the Bottom Line on Momentum vs Kinetic Energy?
Energy and momentum are two views of the same arrow, and they agree until resistance stops being constant. Bone, hide and a bent shaft all make it stop being constant. That is why the arrow with 4% less energy and 23% more momentum models out ahead of its faster cousin on hard targets.
Weigh the arrow for the toughest shot you would take, then check the speed cost with the Arrow Weight vs Speed guide and the Arrow Momentum Calculator. Keep an eye on kinetic energy too. It still tells you whether your bow is doing its job.
Frequently Asked Questions
How much momentum do you need to kill an elk with a bow?
A working floor for elk-class game is about 0.56 slug·ft/s, and 0.60 to 0.65 gives real margin when a shoulder bone is a realistic obstacle. A 550 gr arrow at 250 fps lands at 0.611. A 450 gr arrow at 280 fps sits at 0.559, right at the floor. These are ArcheryEra planning figures built from the model and the ranges bowhunters discuss, not a legal or lab standard. Lower figures circulate too: the mechanical vs fixed broadhead guide cites about 0.40 as the community entry threshold for running a mechanical head on elk-sized game. The pass-through model on this site agrees: about 0.39 reaches elk vitals and about 0.61 passes through with a fixed head at 12% FOC. Read those as minimums for a clean broadside with no bone, and 0.56 to 0.60 as the planning range that leaves room for bone and angles. Pair the weight with 12 to 16% FOC and a sharp, aligned head.
Can an arrow have high kinetic energy and still fail to penetrate?
Yes. Energy counts everything the arrow carries, but bone, a flexing shaft and a deploying blade each spend part of it before it becomes forward cutting. A 350 gr arrow at 320 fps carries 79.6 ft·lb, more than a 550 gr arrow at 250 fps (76.3 ft·lb), yet it carries 19% less momentum and carries an editorial bone score of 4.0 against 9.2. Energy ranks the bow. Momentum, FOC and head geometry rank what happens at the target.
Does arrow weight change how efficient a bow is?
Yes. Part of a bow’s stored energy goes into moving its own limbs and string. A light arrow is gone quickly and the limbs keep more of that energy as their own motion; a heavier arrow takes a larger share. Kooi’s virtual-mass treatment models the bow’s moving parts as extra mass on the arrow, and ArcheryEra’s calculators use 30 grains for it. Applied to a 350 gr arrow at 320 fps, that rule gives about 259 fps at 550 gr: a 19% speed loss for a 57% weight gain, with about 3% more kinetic energy.
Does kinetic energy still matter for bowhunting?
Yes, for three jobs: comparing bows and setups on one scale, meeting the states that write energy minimums into hunting rules, and describing soft-tissue work when nothing hard is in the way. It is a weak sole predictor for bone. I use energy as the sanity check and momentum as the selector.
How do you convert slug·ft/s to kg·m/s?
Multiply by 4.448, which is 14.594 kg per slug times 0.3048 m per foot. A momentum of 0.611 slug·ft/s equals 2.72 kg·m/s.
Is a 350 grain arrow too light for deer?
Not automatically. At 320 fps a 350 gr arrow carries 79.6 ft·lb and 0.497 slug·ft/s, below the 0.55 to 0.58 range I would plan around for whitetail. On a broadside lung shot with no bone and a sharp, aligned fixed head it can work, and the pass-through simulator above shows deer-class odds in soft tissue. Angled shots and shoulder bone are where the thin margin shows. Confirm your state’s legal minimums too.
Hey, what's up? Burak here. Archery addict, board game geek, Daft Punk fan.