acalculator

What is my arrow speed?

Type your bow's IBO rating and your setup. The arrow speed calculator estimates how fast your arrow flies, and its kinetic energy and momentum.

Your numbers

Arrow speed (ft/s)
276.7

Your arrow flies at about 276.7 ft/s with 68 ft·lbf of kinetic energy.

Arrow speed (m/s)
84.3
Kinetic energy (ft·lbf)
68
Kinetic energy (J)
92.2
Momentum (slug·ft/s)
0.491
Momentum (kg·m/s)
2.186
Arrow grains per pound
6.67

Arrow speed (ft/s): 276.7. Your arrow flies at about 276.7 ft/s with 68 ft·lbf of kinetic energy.

How to calculate

Estimates the speed of an arrow in ft/s from the bow’s IBO rating, your draw length, draw weight, arrow weight and string weight, with its kinetic energy and momentum.

Example with the default inputs (IBO speed rating (ft/s) 330, Draw length (in) 28, Peak draw weight (lb) 60, Arrow weight (grains) 400, Weight on the string (grains) 0): Your arrow flies at about 276.7 ft/s with 68 ft·lbf of kinetic energy.

Method: Speed (ft/s) = IBO + 10 × (draw length − 30) − (arrow weight − 5 × draw weight) ÷ 3 − string weight ÷ 3; KE = ½ m v²; momentum = m v.

  • The IBO rating is measured at 70 lb, a 30 in draw, a 350 grain arrow (5 grains per pound) and nothing on the string.
  • The rules of thumb are linear; real bows differ, so a chronograph gives the true speed.
  • Arrows lighter than 5 grains per pound of draw weight are outside the rules (and below the IBO test weight).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. IBO speed rating (ft/s) 330, Draw length (in) 30, Peak draw weight (lb) 70, Arrow weight (grains) 350, Weight on the string (grains) 0 gives Arrow speed (ft/s) 330, Arrow speed (m/s) 100.584, Arrow grains per pound 5.Source: Sunrise Archery, Understanding Bow Speeds (IBO speed rating: 70 lb, 30 in draw, 350 grain arrow). https://sunrisearchery.com/resources/understanding-bow-speeds/
  2. IBO speed rating (ft/s) 330, Draw length (in) 28, Peak draw weight (lb) 60, Arrow weight (grains) 400, Weight on the string (grains) 0 gives Arrow speed (ft/s) 276.666667, Kinetic energy (ft·lbf) 67.973545, Momentum (slug·ft/s) 0.491375.Source: N1 Outdoors, Arrow Speed Calculator (draw length ±10 ft/s per inch from 30 in; −1 ft/s per 3 grains of arrow weight above 5 × draw weight; −1 ft/s per 3 grains on the string). https://n1outdoors.com/arrow-speed-calculator/; Sunrise Archery, Understanding Bow Speeds (IBO speed rating: 70 lb, 30 in draw, 350 grain arrow). https://sunrisearchery.com/resources/understanding-bow-speeds/ (this setup shoots about 275 ft/s); NIST SP 811 (2008), Appendix B.8 (1 grain = 64.79891 mg; 1 ft = 0.3048 m; 1 lbf = 4.4482216152605 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8
  3. IBO speed rating (ft/s) 340, Draw length (in) 29, Peak draw weight (lb) 70, Arrow weight (grains) 425, Weight on the string (grains) 12 gives Arrow speed (ft/s) 301, Kinetic energy (J) 115.901632, Kinetic energy (ft·lbf) 85.484657.Source: N1 Outdoors, Arrow Speed Calculator (draw length ±10 ft/s per inch from 30 in; −1 ft/s per 3 grains of arrow weight above 5 × draw weight; −1 ft/s per 3 grains on the string). https://n1outdoors.com/arrow-speed-calculator/; NIST SP 811 (2008), Appendix B.8 (1 grain = 64.79891 mg; 1 ft = 0.3048 m; 1 lbf = 4.4482216152605 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8

How it works

  • Speed (ft/s) = IBO + 10 × (draw length − 30) − (arrow weight − 5 × draw weight) ÷ 3 − string weight ÷ 3. Draw length is in inches, draw weight in pounds, arrow and string weights in grains.
  • When the arrow weighs less than 5 grains per pound of draw weight (arrow weight < 5 × draw weight) there is no answer: the rules only cover heavier arrows. A speed of 0 or below has no answer.
  • Speed (m/s) = ft/s × 0.3048.
  • Kinetic energy (J) = ½ × m × v², with m = arrow grains × 0.00006479891 kg and v in m/s. Foot-pounds = J ÷ (0.3048 × 4.4482216152605).
  • Momentum (kg·m/s) = m × v; slug·ft/s (lbf·s) = kg·m/s ÷ 4.4482216152605.
  • Grains per pound = arrow weight ÷ draw weight.

Every step is an exact fraction of the typed decimals; each output is rounded once. Speeds, energies show with at most 1 decimal, momentum with at most 3, grains per pound with at most 2, rounded half up.

Assumptions

  • IBO 100 to 500 ft/s; draw length 15 to 40 in; draw weight 10 to 150 lb; arrow 50 to 2,000 grains; string weight 0 to 500 grains.
  • The adjustments are linear rules of thumb; they do not model brace height, cams or let-off.

Worked examples by hand

The IBO setup: 330 ft/s, 30 in, 70 lb, 350 gr. No change: 330 ft/s = 100.584 m/s; 350 ÷ 70 = 5 grains per pound.

330 ft/s bow, 28 in, 60 lb, 400 gr. 330 + 10 × (28 − 30) − (400 − 300) ÷ 3 = 330 − 20 − 33.33 = 276.67 ft/s (84.328 m/s). m = 400 × 0.00006479891 = 0.025919564 kg; KE = ½ × 0.025919564 × 84.328² = 92.16 J = 67.97 ft·lbf; momentum = 0.025919564 × 84.328 = 2.1857 kg·m/s = 0.491 slug·ft/s.

340 ft/s bow, 29 in, 70 lb, 425 gr, 12 gr on the string. 340 − 10 − (425 − 350) ÷ 3 − 12 ÷ 3 = 340 − 10 − 25 − 4 = 301 ft/s (91.7448 m/s). m = 0.02753953675 kg; KE = 115.90 J = 85.48 ft·lbf.

Other questions people ask

What is the IBO speed rating?

It is the speed a bow shoots under a standard test: 70 lb peak draw weight, 30 in draw length and a 350 grain arrow (5 grains per pound), with nothing on the string. Most setups are slower than the rating.

How do I estimate my arrow speed?

Start from the IBO rating. Add or take away 10 ft/s for each inch of draw length above or below 30 in. Take away 1 ft/s for every 3 grains of arrow weight above 5 grains per pound of draw weight, and 1 ft/s for every 3 grains on the string.

How fast is a 330 ft/s bow at 28 in and 60 lb?

With a 400 grain arrow: 330 − 2 × 10 − (400 − 5 × 60) ÷ 3 = 276.7 ft/s. Sunrise Archery gives about 275 ft/s for the same setup.

How is arrow kinetic energy worked out?

Kinetic energy is ½ m v². With m in kilograms (1 grain = 64.79891 mg) and v in m/s it comes in joules; divide by 1.3558 for foot-pounds. A 400 grain arrow at 276.7 ft/s carries about 68 ft·lbf.

Why can my arrow not be lighter than 5 grains per pound?

The IBO test arrow is 5 grains per pound of draw weight, and the speed rules only cover heavier arrows. Bow makers warn against arrows below their minimum weight, because a light arrow leaves much of the energy in the bow.

How accurate is this estimate?

The rules are averages. Brace height, cam design, let-off and string accessories also change the speed, so a chronograph gives your true speed. Use the estimate to compare setups.