Arrow Momentum Calculator
Momentum predicts how hard your arrow is to stop. Enter weight and speed for the slug·ft/s figure — and the kinetic energy alongside it, because the two tell different stories.
How Arrow Momentum Is Calculated
Momentum is mass times velocity — no squares, no halves. In archery units it reduces to:
The constant folds the grains-to-slugs conversion into one number. Because speed enters only to the first power, momentum rewards weight in a way kinetic energy does not — which is the entire heavy-arrow debate, and the subject of the next section.
Kinetic Energy vs Momentum
Dr Ed Ashby spent decades shooting arrows into real game animals and recording what penetrated and what did not. His conclusion, published through the Ashby Bowhunting Foundation: once an arrow has adequate energy, momentum and arrow build predict penetration far better than kinetic energy does. The reasoning is physical. Hide, hair and bone resist the arrow by spending its momentum; energy figures, inflated by the squared speed term, flatter light fast arrows that the resistance stops quickly anyway.
The fair counterpoint: momentum is not magic either. A very heavy, very slow arrow arcs hard, shrinks your margin for range-estimation error, and still fails with a dull or fragile broadhead. Ashby's own framework treats momentum as one factor among several — arrow integrity, broadhead design and FOC among them. This site shows both numbers on every result so you can weigh the trade yourself; the kinetic energy calculator makes the energy case, and the FOC calculator covers the balance factor.
| Build | Speed | Kinetic energy | Momentum |
|---|---|---|---|
| 400 gr — light & fast | 300 fps | 80.0 ft-lb | 0.53 |
| 450 gr — the middle way | 286 fps | 81.8 ft-lb | 0.57 |
| 600 gr — heavy & slow | 245 fps | 80.0 ft-lb | 0.65 |
Three builds, near-identical energy — and the heavy arrow carries about 23% more momentum. That gap, not the energy figure, is what Ashby's testing says shows up on game.
Momentum Guidance
| Momentum | Reads as |
|---|---|
| Under 0.35 | Light and fast — targets and small game |
| 0.35–0.44 | Deer class with a good broadhead |
| 0.45–0.54 | Solid large-game momentum — elk, bear |
| 0.55 + | Heavy-arrow country — the toughest game |
Momentum Worked Examples
450 grains at 280 fps: 450 × 280 ÷ 225,400 = 0.56 slug·ft/s — comfortably past the deer band with energy to spare.
A 550-grain wood arrow at 175 fps from a longbow: 550 × 175 ÷ 225,400 = 0.43. Slow by compound standards, yet squarely in deer momentum — the traditional bowhunter's whole point.
A 450-grain bolt at 383 fps: 450 × 383 ÷ 225,400 = 0.76. Crossbow momentum is abundant; broadhead choice and accuracy decide the outcome. Estimate your own bolt speed on the crossbow calculator.
Momentum FAQs
How much momentum do I need for deer?
On Ashby-style guidance, arrows around 0.40 slug·ft/s and up with a quality broadhead are the deer class; 0.45–0.55 covers elk-sized game, and heavy-arrow builds for the toughest game run higher. A 450-grain arrow at 280 fps makes 0.56 — most modern compound setups are already in large-game momentum territory.
What does slug·ft/s actually mean?
Momentum is mass times velocity. In archery units — grains × fps ÷ 225,400 — the result is expressed in slug·ft/s, the imperial momentum unit. You never need to handle a slug of anything; just treat the number as a score where higher means the arrow is harder to stop.
Why do heavy arrows penetrate better if the KE is the same?
Because penetration is a momentum problem. Two arrows with equal kinetic energy do not resist slowing equally: the heavier, slower one carries more momentum, and resistance — hide, hair, bone — spends momentum, not energy. That is the heart of Dr Ed Ashby’s decades of penetration testing, and it is why this site never shows KE alone.
How is arrow momentum calculated?
Momentum in slug·ft/s is arrow weight in grains multiplied by speed in fps, divided by 225,400. Unlike kinetic energy, speed is not squared — double the weight at the same speed doubles the momentum, which is exactly the heavy-arrow argument in one line of arithmetic.
Does momentum fall off at distance like KE does?
Yes, but more gently. Momentum drops in direct proportion to speed, while KE drops with the square of speed — so at 40 yards an arrow has lost roughly 9% of its energy but only about 4–5% of its momentum on this site’s drag model. Heavy arrows keep their downrange advantage.
- Ashby Bowhunting Foundation — Dr Ed Ashby’s arrow penetration research — the source of the momentum and FOC guidance
- Easton Archery — shaft selection charts — the reference spine-selection and arrow-building charts this site’s groupings follow
- Gold Tip — arrow university and spine charts — manufacturer spine charts and arrow-weight data used to cross-check the tables