Arrow setup inputs
Formula used
Momentum: p = m × v
Kinetic energy: KE = 0.5 × m × v²
Impulse: I = Δp. For a fully stopped arrow, impulse is approximately equal to the arrow momentum.
Average impact force: F = I / t, where t is impact duration in seconds.
Estimated deceleration: a = v² / (2d), where d is stopping distance.
Estimated stopping time: t = v / a
These calculations assume straight-line motion and simplified stopping behavior. Real penetration and damage also depend on broadhead design, arrow tune, angle, and target material.
How to use this calculator
Enter the arrow mass and choose the matching mass unit.
Enter arrow speed and select the correct speed unit.
Add arrow count if you want total volley momentum and total energy.
Use impact duration to estimate average force during deceleration.
Use stopping distance to estimate deceleration and stopping time.
Pick your preferred decimal precision, then press the calculate button.
Review the results above the form, inspect the graph, and export your summary as CSV or PDF.
Example data table
| Arrow Mass | Speed | Momentum (kg·m/s) | Momentum (slug·ft/s) | Kinetic Energy (J) | Kinetic Energy (ft·lb) |
|---|---|---|---|---|---|
| 350 grains | 250 fps | 1.7282 | 0.3885 | 65.8263 | 48.5510 |
| 400 grains | 280 fps | 2.2110 | 0.4971 | 94.3116 | 69.5609 |
| 500 grains | 300 fps | 2.9626 | 0.6661 | 135.4192 | 99.8816 |
Frequently asked questions
1. What does arrow momentum tell me?
Arrow momentum measures how much motion the arrow carries. Higher momentum often helps penetration comparisons, especially when arrow mass stays substantial and flight remains efficient.
2. Is momentum more important than kinetic energy?
They describe different things. Momentum is useful for penetration discussion, while kinetic energy shows work potential. Archers usually compare both together for a fuller performance picture.
3. Why does arrow mass matter so much?
Momentum increases directly with mass. A heavier arrow can keep useful momentum even if speed drops, which is why mass changes often produce noticeable hunting setup differences.
4. Why include impact duration?
Impact duration lets the calculator estimate average force from impulse. Shorter stopping times produce larger average forces, though real targets rarely stop arrows uniformly.
5. What is stopping distance used for?
Stopping distance helps estimate deceleration and stopping time using simple motion equations. It is a model, not a guaranteed penetration depth prediction.
6. Which mass unit is best for archery?
Grains are most common for arrows and broadheads. This calculator also supports grams, kilograms, and pounds for classroom problems or engineering-style comparisons.
7. Can I compare multiple arrows at once?
Yes. Enter arrow count to estimate total volley momentum and total energy. Per-arrow momentum still remains the key number for a single projectile.
8. Are these results enough for bow tuning?
No. Good tuning also depends on spine, broadhead alignment, draw setup, arrow straightness, paper tuning, and real-world grouping results.