Arrow Speed Calculator — Bow Velocity & Kinetic Energy

Formula

How this is calculated

A bow stores mechanical energy in its limbs when you draw it. For a bow with a roughly linear force-draw curve, the stored energy approximates a triangle: E_stored = ½ × draw_weight × draw_length, measured in inch-pounds. One inch-pound equals 0.11298 J, so a 60 lb bow at 28 inches stores about 75 J. Not all of this energy reaches the arrow — some remains in the limbs, string and cables after the shot. The fraction transferred is the bow efficiency η (typically 65–80%), giving E_arrow = η × E_stored.

With the arrow's kinetic energy known, speed follows from the kinetic energy definition KE = ½mv², rearranged to v = √(2·KE/m). Arrow mass is entered in grains (1 grain = 0.0000648 kg), the conventional archery unit. For an 80% efficient 60 lb / 28 in compound bow shooting a 400 grain arrow, this gives about 260 fps, consistent with real-world chronograph data for that setup.

The IBO (International Bowhunting Organization) speed rating uses standardised conditions: 70 lb draw weight, 30 in draw length, 350 grain arrow with 80% compound efficiency. The calculator shows an IBO-equivalent speed for your bow at the same efficiency, so you can benchmark against manufacturer specs. Accuracy depends on how closely the linear force-draw approximation fits your specific bow — single-cam compounds with high let-off may store slightly less energy than this model predicts, while traditional bows with heavier limbs may be slightly lower.