What this calculator does
Arrow speed on its own does not say much about what an arrow can do on impact. A light arrow at high speed and a heavy arrow at lower speed can carry very similar energy, which is why bowhunting guidance is written in terms of kinetic energy rather than speed alone. This arrow speed calculator takes a measured or chronographed speed together with total arrow weight and works out the kinetic energy and momentum behind it.
Predicting arrow speed from bow draw weight, draw length and cam design is not reliable without a chronograph, because the same bow specification can shoot noticeably differently between individual bows, strings and arrow setups. Once you have an actual measured speed, though, the energy and momentum calculations below are exact physics, not an estimate.
The formula
Kinetic energy in foot-pounds is the arrow weight in grains multiplied by the speed in feet per second squared, divided by 450,240, a constant that converts grains and fps into the standard ft-lbs unit archers use. The same energy is also shown in joules, and a momentum index is given in slug-fps, a measure some archers use alongside kinetic energy because it behaves differently with penetration.
| Term | Meaning |
|---|---|
| Grain (gr) | The standard unit for arrow and arrowhead weight; 7,000 grains make one pound. |
| fps | Feet per second, the standard unit for arrow speed, usually read from a chronograph. |
| KE | Kinetic energy, the energy of the arrow in motion, which does the work of penetration. |
| Momentum | Mass times velocity; unlike kinetic energy it does not fall away as fast when speed drops, which matters for deep penetration. |
The inputs explained
| Field | What to enter |
|---|---|
| Total arrow weight (gr) | Total finished arrow weight, including the point, insert, fletching and nock, not just the bare shaft. |
| Arrow speed (chronographed) (fps) | Arrow speed as measured by a chronograph, or the speed printed on a spec sheet if no chronograph reading is available. |
When to use it
Checking hunting energy minimums
Many jurisdictions and ethical hunting guides quote a minimum kinetic energy for a given game size rather than a minimum speed, because energy is what determines penetration.
Comparing two arrow builds
A heavier arrow shot from the same bow usually loses some speed but often gains kinetic energy and momentum, since weight increases faster than speed drops within normal ranges.
Reading a chronograph session
After a chronograph reading, converting straight to kinetic energy shows how much margin there is above or below a target energy level, rather than comparing raw fps numbers.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How kinetic energy changes with arrow speed at a fixed weight
The same 400 grain arrow at a range of chronographed speeds.
| Arrow speed | Kinetic energy | Momentum index |
|---|---|---|
| 220 fps | 43.0 ft-lbs | 0.391 slug-fps |
| 240 fps | 51.2 ft-lbs | 0.426 slug-fps |
| 260 fps | 60.1 ft-lbs | 0.462 slug-fps |
| 280 fps | 69.7 ft-lbs | 0.497 slug-fps |
| 300 fps | 80.0 ft-lbs | 0.533 slug-fps |
| 320 fps | 91.0 ft-lbs | 0.568 slug-fps |
How kinetic energy changes with arrow weight at a fixed speed
A range of arrow weights all shot at the same 280 fps.
| Arrow weight | Kinetic energy | Typical hunting guidance |
|---|---|---|
| 300 gr | 52.2 ft-lbs | in the range typically cited for larger or tougher game |
| 350 gr | 60.9 ft-lbs | in the range typically cited for larger or tougher game |
| 400 gr | 69.7 ft-lbs | well into the range cited for the largest game |
| 450 gr | 78.4 ft-lbs | well into the range cited for the largest game |
| 500 gr | 87.1 ft-lbs | well into the range cited for the largest game |
| 550 gr | 95.8 ft-lbs | well into the range cited for the largest game |
Questions
What kinetic energy is needed for deer hunting?
Guides commonly cite roughly 25 to 40+ ft-lbs as adequate for deer-sized game with a well-placed shot and sharp broadhead, though local regulations and ethical hunting organisations vary in their exact figures and should be checked directly.
Why does this calculator not predict speed from my bow specs?
Draw weight, draw length and cam design only give a rough guide to arrow speed; the same specification can shoot several fps differently between individual bows and setups, so a genuine chronograph reading is the only reliable input for this calculation.
Is momentum or kinetic energy more important?
Both matter. Kinetic energy is the standard figure quoted for hunting minimums, but momentum falls away more slowly as an arrow decelerates through tissue, which is why some archers weight momentum more heavily when comparing heavy, slow setups against light, fast ones.
Does arrow speed alone tell you how hard an arrow hits?
No. Two arrows at the same speed but different weights carry different energy, and two arrows at the same energy can come from very different speed and weight combinations, so energy and momentum are the more meaningful figures.
For the general physics behind this, see the kinetic and potential energy calculator and the momentum and impulse calculator.