How this instrument works
Kinetic energy is the energy of motion, ½mv², and once the string releases, an arrow carries that energy away as speed. Solve the equation for v and you get v = √(2·KE⁄m): speed is the square root of twice the delivered energy divided by the arrow's mass. That square root is not decorative — it means energy and speed are not proportional. Doubling the kinetic energy delivered to the same arrow multiplies its speed by only √2, about 1.41, because energy grows with the square of velocity, not with velocity itself.
The one-half in the energy term has a real origin: Gaspard-Gustave Coriolis fixed it at ½mv² in his 1829 textbook on machine mechanics, replacing Leibniz's older 'vis viva,' which had used mv² without the fraction. In archery, the KE side of the equation is what a chronograph and a scale let you find out indirectly — clock the arrow's actual speed, weigh the arrow, and ½mv² reports how much energy the bow truly delivered, as distinct from the energy it merely stores at full draw.
The formula assumes every joule entered reaches the arrow, which is an idealization. Real bows lose some stored energy to limb vibration, string mass, and hand shock, so a static draw-energy figure will always overstate the speed this instrument returns; the honest input is measured, delivered kinetic energy. There is also a trade worth knowing: at fixed KE a heavier arrow comes out slower by this formula, yet its momentum, m·v, actually rises with mass — which is why hunters often pick heavier arrows for penetration even as the speed reading drops.
- Enter the delivered energy in "Kinetic energy at the bow," in joules — ideally a measured figure, not just the bow's static draw-weight rating — or switch to kJ for large values.
- Enter "Arrow mass" in grams, the field's default, or switch its unit menu to kilograms.
- Read "Arrow speed" in metres per second, or switch the unit to feet per second to compare against a manufacturer's chronograph numbers.
- Sanity-check the result: halving the arrow mass at the same energy should raise speed by a factor of √2, not by a factor of 2.
Worked example — a 70 J bow and a 25-gram arrow
A compound bow delivers 70 J of kinetic energy to a 25-gram (0.025 kg) arrow. Solving v = √(2·KE⁄m) gives v = √(2 × 70 ⁄ 0.025) = √5600 = 74.8331477355 m/s, which the instrument displays as about 74.8 m/s.
In the units archers actually talk in, that reads as about 245 ft/s — a realistic figure for a modern compound bow — and the 70 J of delivered energy works out to roughly 51.6 ft-lb, comfortably clear of the light benchmarks some hunters use for deer-sized game, a reminder that delivered energy, not draw weight alone, is what a chronograph confirms downrange.
Questions
What is the IBO speed rating printed on a bow's spec sheet?
It's a manufacturer's chronograph figure taken under the International Bowhunting Organization's rule: an arrow weighing five grains per pound of the bow's draw weight, with no fixed draw length required. The stricter ATA standard instead fixes all three variables — a 70-pound draw weight, a 30-inch draw length, and a 350-grain arrow — which is why ATA numbers compare bows more fairly than IBO ones do.
Why doesn't doubling the kinetic energy double the arrow's speed?
Because kinetic energy scales with the square of velocity, not with velocity itself. Solving KE = ½mv² for v puts a square root over the energy term, so multiplying KE by 2 only multiplies speed by √2 ≈ 1.41. The 70 J, 74.8 m/s arrow above reaches just 105.8 m/s at 140 J — not 149.7 m/s — because a true doubling of speed needs four times the delivered energy.
How much kinetic energy does an arrow need for hunting deer or elk?
There's no single legal figure — most states regulate broadhead type and draw weight rather than energy — but archery equipment makers commonly cite around 25 ft-lb (34 J) as adequate for deer-sized game and roughly 65 ft-lb (88 J) for tougher animals like elk or black bear. Treat those as informal benchmarks and check your state wildlife agency's actual rules before hunting.
Does a heavier arrow always leave the bow slower?
At a fixed kinetic energy, yes — v = √(2KE⁄m) falls as mass rises. But momentum, m·v, actually increases with mass at fixed KE, because it works out to √(2·KE·m), which grows with the square root of mass even as speed falls. That is why hunters often favor heavier arrows for penetration despite the lower speed reading: they are trading velocity for momentum on purpose.
Can I enter arrow mass in grains instead of grams?
Not directly — the mass field's unit menu offers grams and kilograms only. Archers who weigh arrows in grains, the traditional archery unit, can convert with an exact factor: there are 7000 grains to the pound, so dividing grains by 15.432 gives grams. A typical 400-to-500-grain hunting arrow works out to roughly 26 to 32 grams.
Why might a chronograph reading disagree with this calculator?
Usually because the kinetic-energy figure entered isn't the energy actually delivered to that arrow. Bow specs often list stored energy at full draw, but limb vibration, string mass, and hand shock all subtract from that before release, so the true delivered KE — and the speed calculated from it — is normally a little lower than a static rating implies.