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 (Estimated)
The following (approximate) formula can be used to estimate arrow speed in feet per second (FPS) from draw weight, draw length, and arrow weight. It assumes a linear draw-force curve and a typical bow efficiency of η = 0.80.
FPS = \sqrt{\frac{\eta \cdot DW \cdot DL \cdot 7000 \cdot g}{12 \cdot W}}Variables:
- FPS is the arrow speed in feet per second (ft/s)
- W is the arrow weight (mass) in grains
- DW is the draw weight at full draw in pounds-force (lbf)
- DL is the draw length in inches
- η is bow efficiency (dimensionless). This calculator assumes η = 0.80
- g is standard gravity (32.174 ft/s²) used for unit conversion when converting grains (lbm) to slugs
To estimate FPS, convert draw length to feet (DL ÷ 12), apply the formula above, and take the square root. For more accurate results, use a chronograph or the manufacturer’s IBO/ATA speed rating adjusted for your specific setup.
What is a Bow Fps?
Bow FPS (feet per second) is a common way to describe the speed at which an arrow leaves the bow. It matters for both hunting and target shooting because arrow speed affects trajectory (drop) and, along with arrow mass, affects kinetic energy and momentum. Arrow speed is influenced by the bow’s draw weight and draw length, arrow weight, and the bow’s efficiency/design. Higher FPS generally produces a flatter trajectory, but draw difficulty is determined by the bow’s draw force (draw weight and force curve), not FPS by itself.
How to Calculate Bow Fps?
The following steps outline how to estimate Bow FPS using the simplified formula above.
- Determine the draw weight of the bow at full draw (lbf).
- Determine the draw length (in).
- Determine the arrow weight (grains).
- Use the formula: FPS = √( η × DW × DL × 7000 × g ÷ (12 × W) ) (with η ≈ 0.80 and g = 32.174 ft/s²).
- Calculate the Bow FPS (estimated), then compare with a chronograph measurement if available.
Example Problem:
Use the following variables as an example problem to test your knowledge (using η = 0.80):
Draw weight of the bow (lbf) = 50
Draw length (in) = 28
Arrow weight (grains) = 350
Estimated arrow speed ≈ 245.1 ft/s
