Arrow Kinetic Energy Calculator
Kinetic energy (ft-lb) equals finished arrow weight in grains times speed in fps squared, divided by 450,240. 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 energy is your arrow carrying?
Move either slider and the result recalculates instantly, using the exact same kinetic-energy 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 kinetic-energy number that surprised you, or an idea for a new tool?
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Want your arrow's momentum too?
Kinetic energy and momentum answer different questions, so this tool sticks to one number. For the other side of the pair, use the Arrow Momentum Calculator — same weight and speed, one line of maths.
Guide
What Kinetic Energy Actually Tells You
💡 Quick Summary
Core Insight: Kinetic energy (ft-lb) = arrow weight (grains) × speed (fps)² ÷ 450,240. Speed is squared, so a small speed change moves the number more than an equivalent weight change.
Ideal For: Archers who already have a chronographed or estimated speed and want a fast, no-frills energy figure before deciding whether to dig into the fuller downrange picture.
How Does Speed Change Kinetic Energy Compared to Weight?
Speed sits squared in the formula; weight sits by itself. Push speed up 10% and energy climbs roughly 21%. Push weight up 10% and energy only climbs about 10%.
That is the whole reason light, fast arrows and heavy, slower arrows can land close to the same kinetic-energy figure despite feeling completely different off the string. Neither approach is wrong — they are trading energy for a flatter trajectory, or trading a flatter trajectory for retained momentum, and the Kinetic Energy, Momentum & Pass-Through Calculator is where that trade plays out at an actual shot distance.
Why Doesn't Kinetic Energy Alone Tell the Whole Penetration Story?
Kinetic energy is exact physics — there is nothing to argue about once weight and speed are known. What it does not capture is how the arrow behaves once it meets resistance: that depends on momentum, broadhead geometry and construction, arrow FOC, and the target itself.
Treat this number as one input to a bigger picture, not a verdict on its own.
⚠️ What This Number Doesn't Tell You
A kinetic-energy figure by itself does not predict penetration or make a lethality claim. Momentum, 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 kinetic energy?
Kinetic energy (ft-lb) equals finished arrow weight in grains times speed in fps squared, divided by 450,240. That constant folds in the grains-to-slugs conversion and standard gravity, so the formula stays in the units archers actually measure — grains and fps.
What is a good kinetic energy for hunting deer or elk?
Published guidelines commonly cite roughly 25–41 ft-lb as adequate for deer-class game and 42 ft-lb or more for elk-class and larger. Treat these as reference bands, not guarantees — broadhead design, shot placement and FOC all move the real outcome.
Does kinetic energy alone determine penetration?
No. Kinetic energy describes the energy the arrow is carrying, not how deep it drives once it meets resistance — that also depends on momentum, broadhead geometry and construction, FOC and the target itself. ArcheryEra's Simulation Lab models those factors together instead of reading penetration off energy alone.
🎯 Want to See What That Number Means at Distance?
This calculator answers "how much energy does my arrow have right now" — a clean, instant number. It doesn't model what happens to that energy 20 or 40 yards downrange, or how it interacts with a specific broadhead and game animal.
👉 Recommendation: Explore downrange kinetic energy, momentum, 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 73.1 ft·lb 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.
 Quick Tools |
 Simulation Lab |
|---|---|
| Arrow Speed & Performance Calculator | Arrow Build & GPI Weight Calculator |
| Draw Length Calculator | Dynamic Spine & Shaft Flex Calculator |
| Arrow Weight Calculator | Arrow FOC & Balance Point Optimizer |
| Arrow Shaft Finder | Paper Tune Root-Cause Diagnostic |
| Recurve Arrow Spine Calculator | Broadhead Flight & Tuning Stability Checker |
| Carbon Arrow Spine Calculator | Tree-Stand & Angled Shot Distance Compensator |
| Wood Arrow Spine Calculator | Arrow Trajectory & Sight-Pin Visualizer |
| Arrow Kinetic Energy CalculatorYou are here | Kinetic Energy, Momentum & Pass-Through Calculator |
| Arrow Momentum Calculator | |
| Bow Size Calculator | |
| Nock & Insert Fitment Finder |
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