Arrow Momentum Calculator
Momentum (slug-ft/s) equals finished arrow weight in grains times speed in fps, divided by 225,218. Enter your two numbers below and the result updates instantly — no sign-up, no saved setup required.
ArcheryEra's calculators are built and maintained by a mechanical engineer with 8+ years of archery-domain experience. Models, assumptions and limitations are shown, not hidden.
Want to see the exact formulas and physics behind this calculator? Read our Methodology & Assumptions →
Quick Tools
One question, one number: how much momentum is your arrow carrying?
Move either slider and the result recalculates instantly, using the exact same momentum formula as the rest of ArcheryEra's tools.
Useful? This one is free, and staying free. If it saved you a guessing game at the bow, you can put a coffee towards the hosting.
Buy Me a Coffee🗣️ Got a momentum number that surprised you, or an idea for a new tool?
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Want to see the same arrow's kinetic energy?
Momentum and kinetic energy answer different questions, so this tool sticks to one number. For the other side of the pair, use the Arrow Kinetic Energy Calculator — same weight and speed, one line of maths.
Guide
What Momentum Actually Tells You
💡 Quick Summary
Core Insight: Momentum (slug-ft/s) = arrow weight (grains) × speed (fps) ÷ 225,218. Weight and speed count evenly here — neither one dominates the way speed does in the kinetic-energy formula.
Ideal For: Archers comparing a heavier, slower arrow build against a lighter, faster one and wanting the number bowhunters chasing pass-throughs actually watch.
Why Can a Heavier, Slower Arrow Carry More Momentum?
Kinetic energy weights speed twice over; momentum weights weight and speed the same. Add weight to an arrow and its momentum climbs in step, even if the added weight costs it some speed off the bow.
That's the physics behind the heavy-arrow argument for bowhunting: within a sensible weight range, an arrow gives up comparatively little kinetic energy for a real gain in momentum. What it does cost is trajectory — a heavier arrow drops more across a given yardage, which is a separate trade-off the Arrow Trajectory & Sight-Pin Visualizer shows directly.
Is Momentum a Penetration Score?
Momentum tells you how much mass is moving and how fast it's still moving. It's an important part of understanding an arrow's ability to continue moving through resistance, but it is not a penetration score by itself.
Broadhead geometry and construction, FOC, and what the arrow actually meets on impact all factor in — the Kinetic Energy, Momentum & Pass-Through Calculator is where those combine into a full model.
⚠️ What This Number Doesn't Tell You
A momentum figure by itself does not predict penetration or make a lethality claim. It is one input among several — broadhead type, FOC and the target's own resistance all factor into what actually happens on impact — see the Simulation Lab's penetration model for how ArcheryEra weighs them together, and treat its output as a ranking model, not a laboratory measurement.
Frequently Asked Questions
How do you calculate arrow momentum?
Momentum (slug-ft/s) equals finished arrow weight in grains times speed in fps, divided by 225,218. Unlike kinetic energy, speed is not squared here — weight and speed both count evenly.
Why does a heavier arrow carry more momentum even at a lower speed?
Momentum weights mass and velocity equally, so a heavier arrow that gives up some speed can still post a higher momentum figure than a lighter, faster one. Kinetic energy behaves differently because it weights speed twice over, which is why the same two arrows can swap places depending on which number you look at.
Does higher momentum guarantee more penetration?
No. Momentum is an important part of how an arrow continues moving through resistance, but it is not a penetration score by itself — broadhead geometry and construction, FOC, and the target's own resistance all factor in. ArcheryEra's Simulation Lab models those together as a calibrated ranking, not a lab measurement.
🎯 Want to See How Your Momentum Changes With Distance?
This calculator answers "how much momentum does my arrow have right now" — a clean, instant number. It doesn't model how that momentum holds up 20 or 40 yards downrange, or how it interacts with a specific broadhead and game animal.
👉 Recommendation: Explore downrange momentum, kinetic energy, and ArcheryEra's penetration/pass-through model in the Kinetic Energy, Momentum & Pass-Through Calculator →
Check it: a 420 grain arrow at 280 fps reads about 0.522 slug·ft/s on this calculator — the same figure the Arrow Speed & Performance Calculator and the Simulation Lab's Kinetic Energy, Momentum & Pass-Through Calculator produce from the identical inputs, because all three run on the same shared formula.
All Tools & Simulations
Every free calculator on ArcheryEra in one table — answer a single question with a Quick Tool, or chain a full build through the Simulation Lab.
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