Enter any 3 values (arrow speed, arrow weight, draw length, and draw weight) into the calculator to estimate the missing variable. This calculator uses a simplified energy model (assumes a linear draw-force curve and a typical bow efficiency of 80%), so results are approximate and real-world speeds can vary by bow design, cam/limb efficiency, string/arrow setup, and tuning.
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Bow FPS Formula
The bow FPS calculator uses a simplified energy-based model. Internally, it converts values to feet per second, grains, inches, and pounds-force, then solves for the missing value.
- FPS = arrow speed in feet per second
- AW = arrow weight in grains
- DW = draw weight at full draw in pounds-force
- DL_ft = draw length in feet
- DL_in = draw length in inches
- eta = bow efficiency, fixed at 0.80 in this calculator
- g = 32.174 ft/s²
- 7000 = grains per pound-mass
If speed is blank, the calculator estimates bow FPS from arrow weight, draw length, and draw weight. If arrow weight is blank, it rearranges the same formula to estimate the arrow weight needed for the entered speed. If draw length or draw weight is blank, it solves for that missing input using the entered speed and arrow setup.
Bow Speed, Arrow Weight, and Unit Reference
These ranges are general references. Actual bow speed depends on bow design, cam system, string accessories, arrow setup, release quality, and tuning.
| Setup or Result | Typical Range | Notes |
|---|---|---|
| Recreational compound bow speed | 220 to 280 ft/s | Common for moderate draw weight and heavier arrows. |
| Hunting compound bow speed | 250 to 320 ft/s | Depends heavily on arrow weight and draw length. |
| Light arrow | 300 to 400 grains | Usually faster, but may reduce momentum and can be unsafe if too light for the bow. |
| Medium hunting arrow | 400 to 500 grains | Common balance of speed, penetration, and durability. |
| Heavy arrow | 500+ grains | Usually slower, with higher momentum and quieter shooting. |
| Conversion | Value Used |
|---|---|
| 1 m/s to ft/s | 3.28084 ft/s |
| 1 gram to grains | 15.4324 grains |
| 1 kilogram to grains | 15432.4 grains |
| 1 centimeter to inches | 0.393701 inches |
| 1 kgf to lbf | 2.20462 lbf |
Example Bow FPS Calculations
Example 1: Calculate bow speed
You enter an arrow weight of 400 grains, a draw length of 28 inches, and a draw weight of 60 lbf.
The estimated arrow speed is about 251.12 ft/s.
Example 2: Calculate arrow weight
You enter a speed of 280 ft/s, a draw length of 30 inches, and a draw weight of 70 lbf.
The estimated arrow weight is about 402.18 grains.
Bow FPS Calculator FAQ
Why is the calculated FPS different from my bow’s advertised IBO speed?
Advertised IBO speed is measured under specific test conditions, often with a 70 lb draw weight, 30 inch draw length, and a 350 grain arrow. If your draw length is shorter, your arrow is heavier, or your setup has peep sights, silencers, heavier strings, or other accessories, your real speed will usually be lower.
Does a heavier arrow always lower FPS?
Yes, when the same bow and draw settings are used, a heavier arrow normally leaves the bow at a lower speed. The heavier arrow may still carry useful momentum and kinetic energy, but its feet-per-second value will usually be lower than a lighter arrow.
Is this calculator a chronograph replacement?
No. This calculator gives an estimate based on a simplified formula and a fixed 80% efficiency value. A chronograph gives the actual arrow speed for your bow, arrow, string setup, release, and tune. Use the calculator for planning and comparison, not as a final measured speed.
