Calculate arrow speed from bow draw weight and draw length, or from chronograph data. Get kinetic energy, momentum, and game suitability analysis.
Arrow speed determines kinetic energy, trajectory, penetration potential, and effective range — making it the single most important performance metric for archers and bowhunters. This calculator estimates arrow velocity from bow specifications or processes chronograph readings to compute the full ballistic profile.
The calculator uses an energy-transfer model: stored potential energy in the drawn bow limbs is converted to arrow kinetic energy with a user-adjustable efficiency factor. From speed, it derives kinetic energy (ft-lbs and joules), momentum, grains-per-pound ratio, flight time, and gravity drop to the target.
Preset buttons for common bow types (recurve, compound, longbow, crossbow) and an arrow weight comparison table show how changing arrow mass affects the speed-energy-penetration trade-off. A game suitability chart tells you whether your setup meets minimum kinetic energy requirements for different animals, from small game to dangerous game. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Choosing the right arrow weight involves balancing speed against penetration, and this trade-off is hard to calculate mentally. This calculator shows the complete picture — speed, energy, momentum, and game suitability — for any arrow-bow combination.
The arrow weight comparison table makes it easy to see exactly how much speed you sacrifice for a heavier arrow and how much penetrating momentum you gain in return.
Stored energy = ½ × draw_weight × (draw_length / 12) ft-lbs. Arrow speed (fps) = √(2 × delivered_energy × 32.174 / mass_lbs). KE = ½mv². Momentum = mv. Gravity drop = ½gt².
Result: 268 fps, 55.8 ft-lbs KE
A 60 lb compound bow at 30" draw with 78% efficiency delivers ~58.5 ft-lbs to a 350-grain arrow. Speed ≈ 268 fps, producing 55.8 ft-lbs of kinetic energy — sufficient for most North American big game.
Archery physics presents a fundamental trade-off: lighter arrows fly faster but carry less momentum and kinetic energy per unit of frontal area. Heavier arrows are slower but penetrate better due to higher momentum. The optimal balance depends on your application — target archery favors speed for flat trajectory, while hunting benefits from heavy arrows for penetration.
Both KE and momentum matter for hunting. KE measures the total energy available for tissue destruction, while momentum determines how well the arrow maintains its path through resistance. Many experienced bowhunters now focus on momentum (recommending >0.4 slug·ft/s for big game) because it better predicts penetration through bone and hide.
IBO (International Bowhunting Organization) speed ratings are measured at 70 lbs draw weight, 30" draw length, and 350-grain arrow. Your actual speed will differ. For every inch under 30" draw, subtract ~10 fps. For every 10 grains of additional arrow weight, subtract ~5 fps. For every 3 grains of additional string weight (peeps, silencers), subtract ~1 fps.
Most bowhunters aim for 250-300 fps. More important than raw speed is kinetic energy — you need at least 40 ft-lbs for deer and 55+ for elk. Heavy arrows can achieve this at moderate speeds.
Grains per pound (gr/lb) is the ratio of arrow mass to bow draw weight. Under 5 gr/lb is dangerously light and can damage bows. 6-8 gr/lb is standard, 10+ is heavy for maximum penetration.
Momentum = mass × velocity. Although heavier arrows are slower, the mass increase outweighs the velocity decrease. Higher momentum means better penetration through hide, bone, and tissue.
Bow efficiency is the percentage of stored limb energy transferred to the arrow. Modern compounds achieve 78-85%, recurves 65-75%, and longbows 60-70%. Energy lost goes into limb vibration, noise, and heat.
It is a reasonable approximation (±15 fps for compounds). Actual speed depends on cam design, string quality, arrow spine, and other factors. Use a chronograph for precise measurements.
Gravity constantly pulls the arrow downward at 9.81 m/s². The slower the arrow, the longer it is in flight, and the more it drops. At 20m, a 270 fps arrow drops about 4-5 cm.