The bow arrow kinetic energy and FOC calculator gives bowhunters the three numbers that define an arrow’s terminal performance: how much energy it carries, how much momentum drives penetration, and how its weight is balanced toward the front.
How it works
You enter each component’s grain weight — point or broadhead, insert, shaft, fletching, and nock — and the tool sums them into the total arrow weight. From that it computes:
KE (ft-lbs) = (total_grains × speed_fps²) / 450240
Momentum (slug-fps) = (total_grains × speed_fps) / 225218
Front of center is computed from your measured balance point and arrow length:
FOC % = 100 × (balance_point − length / 2) / lengthBoth the balance point and the arrow length are measured from the throat of the nock. A balance point exactly at the midpoint gives 0% FOC; the farther forward it sits, the higher the FOC percentage.
KE vs momentum: which matters more for penetration?
Kinetic energy and momentum are related but measure different things, and they predict different aspects of arrow performance:
- Kinetic energy reflects the arrow’s ability to do work on impact. It is what most bowhunting guides cite for minimum standards by game size.
- Momentum is mass × velocity and better predicts how far the arrow will travel through tissue after impact. A heavy, slower arrow may have the same KE as a light, fast one but will have higher momentum and generally penetrate deeper.
For this reason, experienced hunters moving to larger game (elk, moose, or African plains game) often deliberately build heavier arrows even at the cost of some speed and KE, because momentum is what drives pass-through penetration.
| Game size | Suggested minimum KE | Notes |
|---|---|---|
| Small game (rabbit, squirrel) | 25 ft-lbs | Very low requirement |
| Whitetail deer | 40 ft-lbs | Common minimum; 50+ recommended |
| Elk / large deer | 65 ft-lbs | Allow margin for steep angles |
| Large / dangerous game | 80+ ft-lbs | Momentum equally important |
These are illustrative guidelines widely cited in bowhunting literature, not regulatory thresholds.
FOC categories and their trade-offs
| FOC range | Label | Typical use |
|---|---|---|
| 7–12% | Standard | Target archery, field archery |
| 10–15% | Hunting | Common range for deer hunting; good balance |
| 15–19% | High FOC | Better penetration, more arc; elk and bear |
| 19%+ | Extreme / Ashby | Maximum penetration; significant drop at distance |
Higher FOC improves in-flight stability (the arrow “wants” to fly point-first) and tends to improve penetration on tough hide and bone. The trade-off is a more parabolic trajectory, which makes judging distance more critical at longer ranges.
Worked example
A broadhead setup with a 100-grain tip, 15-grain insert, 360-grain shaft, 15-grain fletching, and 10-grain nock, shot at 265 fps:
- Total weight: 100 + 15 + 360 + 15 + 10 = 500 grains
- KE: (500 × 265²) / 450,240 = (500 × 70,225) / 450,240 ≈ 78 ft-lbs
- Momentum: (500 × 265) / 225,218 ≈ 0.588 slug-fps
At 500 grains this is a mid-to-heavy hunting arrow with solid KE for whitetail through elk at moderate ranges.
Tips
- Keep grains-per-pound above 5 to protect a compound bow from dry-fire-like stress.
- Weigh components on a grain scale rated to ±0.5 grains for accurate totals.
- Measure the balance point on the finished arrow with all components installed, including a nocked string position.
- A sharp, correctly aligned broadhead and precise shot placement matter more than any single number on this calculator.