Arrow Speed Calculator

Estimate arrow velocity, kinetic energy, and momentum from bow draw weight, draw length, and arrow weight using the bow's work-energy (spring-launch) approximation.

Quick Facts

Formula
v = sqrt(efficiency x draw weight x draw length / arrow mass)
Models the bow as a linear spring: stored energy is approximated as half of draw weight times draw length.
Typical efficiency
Compound ~75-85%, recurve ~65-75%, longbow ~55-65%
The remaining stored energy is lost to limbs, string, and arrow-rest friction.

Your Results

Calculated
Arrow speed
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Estimated velocity leaving the bow (fps)
Arrow speed (m/s)
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Same speed in metric units
Kinetic energy
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Arrow energy at the bow (ft-lbs)
Momentum
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Penetration-related quantity (slug-ft/s)

Ready

Enter draw weight, draw length, arrow weight, and bow type, then press Calculate.

Understanding the Arrow Speed Calculator

This tool estimates how fast an arrow leaves the bow using the work-energy principle: the energy stored while drawing the bow converts into the arrow's kinetic energy as the string releases. Because no bow transfers all of its stored energy to the arrow — some is lost to limb vibration, string and cam mass, and friction at the arrow rest — the calculator applies an efficiency factor based on bow type.

The formula

Treating the bow as a linear spring, the work done drawing it back is approximated as half of the peak draw weight times the draw length: Energy ≈ ½ × Draw Weight × Draw Length. Multiplying that by the bow's efficiency and setting it equal to the arrow's kinetic energy (½ × mass × velocity²), then solving for velocity, gives:

v = √(efficiency × Draw Weight × Draw Length ÷ Arrow Mass)

with draw weight converted to newtons, draw length to meters, and arrow weight (given in grains) converted to kilograms before the calculation runs. The result is converted back to feet per second and meters per second for display.

Kinetic energy and momentum

Once speed is known, two more values commonly used in archery follow directly from it:

  • Kinetic energy (ft-lbs): KE = Arrow Weight (grains) × Speed (fps)² ÷ 450,240 — the standard ballistics energy formula used for both bullets and arrows.
  • Momentum (slug-ft/s): Momentum = Arrow Weight (grains) × Speed (fps) ÷ 225,218 — often cited alongside kinetic energy as an indicator of penetration potential, since momentum scales linearly with arrow weight rather than with its square.

Typical efficiency by bow type

  • Compound bows use cams and let-off to store and release energy efficiently, typically transferring around 75-85% of stored energy to the arrow.
  • Recurve bows are mechanically simpler and typically run around 65-75% efficient.
  • Longbows have the least mechanical advantage and typically run around 55-65% efficient.

These are representative ranges, not fixed constants — actual efficiency depends on limb design, arrow rest friction, brace height, and tuning. A manufacturer's published IBO or AMO speed rating (measured under standardized test conditions) will usually be more accurate for a specific bow than this estimate.

Assumptions and limits

This model assumes the bow's force-draw curve is roughly linear, like an ideal spring. That's a simplification: real compound bows have a distinctly non-linear curve because of cam let-off, and recurve or longbow curves are closer to linear but not exact. The formula also ignores arrow spine, fletching drag during the shot, and string or cam mass. Treat the result as a reasonable estimate for comparing setups, not a substitute for a chronograph reading.

Frequently Asked Questions

What formula does this calculator use?
It models the bow as a linear spring: stored energy is approximated as one half of draw weight times draw length, and a bow-type efficiency factor estimates how much of that energy transfers to the arrow. Solving the work-energy equation for velocity gives speed = square root of (efficiency × draw weight × draw length ÷ arrow mass), with units converted to newtons, meters, and kilograms before the calculation.
What is a good arrow speed?
Modern compound bows typically launch hunting-weight arrows around 250 to 320 feet per second, while recurve bows and longbows are usually slower, often in the 150 to 220 fps range. Manufacturer IBO or AMO speed ratings are measured under standardized conditions and are usually more precise than this estimate for a specific bow.
How much kinetic energy does a hunting arrow need?
Bowhunting references commonly cite rough kinetic-energy bands: under about 25 ft-lbs for small game, roughly 25 to 41 ft-lbs for medium game such as deer, about 41 to 65 ft-lbs for medium-to-large game, and 65-plus ft-lbs for the largest or toughest game. These are widely used rules of thumb, not legal standards, so always check local hunting regulations.
Why does my chronographed speed differ from this estimate?
This calculator assumes an idealized linear force-draw curve and a fixed efficiency percentage. Real bows have non-linear draw curves (especially compounds with cam let-off), plus losses from arrow rest friction, string and cam mass, brace height, and tuning, all of which shift actual chronographed speed away from the estimate.

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