Arrow Speed Calculator

An arrow speed calculator estimates how fast an arrow leaves a bow, in feet per second (fps), based on the bow's IBO speed rating and the archer's actual draw length, draw weight, and arrow setup. It also reports the arrow's kinetic energy and momentum at that speed.

What is IBO speed?

IBO speed is a rating that bow manufacturers publish, named after the International Bowhunting Organization. It describes how fast a bow shoots under one fixed set of test conditions. This calculator models those conditions as a 70-pound draw weight, a 30-inch draw length, and an arrow weighing 350 grains (5 grains for every pound of draw weight), which is the reference setup its adjustments are built around.

Almost no archer shoots at those exact settings. A shorter draw length, a lighter draw weight, or a heavier arrow all change the real speed. The calculator starts from the IBO number and adjusts it for the archer's own setup.

How to calculate arrow speed from IBO rating

The estimate uses the calculator's own rule-of-thumb adjustments to convert a bow's IBO rating into a real-world speed. They are not published IBO figures. Each factor that differs from the reference conditions adds or subtracts a set number of feet per second.

• Draw length: add 10 fps for every inch above 30 inches, or subtract 10 fps for every inch below it.
• Draw weight: add 2 fps for every pound above 70 pounds, or subtract 2 fps for every pound below it.
• Arrow weight: the reference arrow weighs 5 grains per pound of draw weight. For every 3 grains the actual arrow weighs above that reference, subtract 1 fps. For every 3 grains below it, add 1 fps.
• Extra string weight: accessories added to the string, such as a peep sight, D-loop, or string silencers, subtract 1 fps for every 3 grains they weigh.

Arrow speed formula

1speed (fps) = IBO speed
2  + (draw length − 30) × 10
3  + (draw weight − 70) × 2
4  − (arrow weight − 5 × draw weight) / 3
5  − extra string weight / 3
6

Speed cannot go below zero; an extremely heavy arrow simply clamps the estimate at 0 fps.

Kinetic energy and momentum

Once the speed is known, kinetic energy and momentum follow from the arrow's total weight in grains (gr) and its speed in feet per second (fps):

1kinetic energy (ft-lb) = arrow weight (gr) × speed (fps)² / 450,240
2momentum (slug·ft/s)   = arrow weight (gr) × speed (fps) / 225,218
3

The constant 225,218 is the number of grains in one slug, the unit of mass that goes with feet and pounds of force. It follows from the NIST conversion factors for the grain and the slug: 14.59390 kg ÷ 0.00006479891 kg ≈ 225,218. The energy constant 450,240 is the value archers traditionally use. It is about 0.04% smaller than twice 225,218, so the difference does not matter in practice.

Kinetic energy describes how much energy the arrow delivers on impact. Momentum describes how well the arrow keeps driving forward through resistance, such as an animal's hide and bone. Hunters often check both figures against a game animal's minimum recommended energy or momentum before choosing a broadhead and arrow combination.

Example

An archer shoots a bow rated at 320 fps IBO speed, set to a 60-pound draw weight and a 29-inch draw length. The arrow weighs 400 grains total, and the string carries 15 grains of accessories.

1. Draw length adjustment: (29 − 30) × 10 = −10 fps
2. Draw weight adjustment: (60 − 70) × 2 = −20 fps
3. Reference arrow weight: 5 × 60 = 300 grains
4. Arrow weight adjustment: −(400 − 300) / 3 = −33.3 fps
5. String weight adjustment: −15 / 3 = −5 fps
6. Estimated speed: 320 − 10 − 20 − 33.3 − 5 = 251.7 fps (76.7 m/s)

At 251.7 fps, the 400-grain arrow carries about 56.3 ft-lb of kinetic energy and about 0.447 slug·ft/s of momentum.

For comparison, a bow shot at the calculator's reference conditions, 70 pounds, 30-inch draw, and a 350-grain arrow, returns the IBO number itself: 320 fps, 79.6 ft-lb of kinetic energy, and 0.497 slug·ft/s of momentum.

How accurate is this estimate?

The formula gives a working estimate, not a measured speed. It ignores factors that also affect real arrow speed, such as bow efficiency, cam timing, temperature, string material, and arrow rest friction. A chronograph, a device that measures an arrow's actual speed as it passes through two sensors, gives the true number for a specific bow and arrow. Archers commonly use the IBO estimate to compare setups or choose arrow weight before confirming the final number on a chronograph.

Frequently asked questions

What does IBO speed mean? IBO speed is a bow's rated speed under a fixed test setup, which this calculator models as a 70-pound draw weight, a 30-inch draw length, and a 350-grain arrow. Manufacturers list this number as a way to compare bows.

Why is my actual arrow speed lower than the IBO rating? Most archers draw less than 70 pounds or shoot arrows heavier than 5 grains per pound, both of which slow the arrow below the IBO number. A shorter draw length also reduces speed.

Does a heavier arrow always mean less kinetic energy? No. A heavier arrow flies slower, but kinetic energy depends on both weight and speed. Under this calculator's rules, a moderately heavier arrow often carries slightly more kinetic energy, because the added weight outweighs the small loss of speed. Momentum rises too.

What is the difference between kinetic energy and momentum? Kinetic energy measures the energy released on impact. Momentum measures the arrow's ability to keep moving forward through resistance. Bowhunters use kinetic energy to judge overall power and momentum to judge penetration.

Can this calculator replace a chronograph? No. It gives an estimate based on the fixed adjustments above. A chronograph measures the arrow's true speed for a specific bow, arrow, and release, and accounts for factors the formula does not, such as bow efficiency and release technique.

What happens if I enter a very heavy arrow? The estimated speed cannot go below zero. If the arrow weight adjustment would push the result below 0 fps, the calculator reports 0 fps instead of a negative number.

References

1. National Institute of Standards and Technology. NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically. NIST SP 811 Appendix B.8 — 1 grain = 6.479891 × 10⁻⁵ kg and 1 slug = 14.59390 kg, so one slug is about 225,218 grains.