Arrow Speed Calculator

An arrow speed calculator estimates how fast an arrow leaves a bow, in feet per second (fps), from the bow's IBO speed rating and the archer's own 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 measures how fast a bow shoots under fixed test conditions: a 70-pound draw weight, a 30-inch draw length, and a 350-grain arrow. That arrow weight is 5 grains for every pound of draw weight.

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 an IBO rating

The estimate uses adjustments that archery technicians have applied for decades. Each factor that differs from the IBO test 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. Subtract 1 fps for every 3 grains the actual arrow weighs above that reference, and add 1 fps for every 3 grains below it.
• Extra string weight: gear added to the string, such as a peep sight, a D-loop, or string silencers, subtracts 1 fps for every 3 grains it weighs.

Arrow speed formula

$v = I + (l - 30) \times 10 + (w - 70) \times 2 - \frac{a - 5 \times w}{3} - \frac{s}{3}$

where v is the estimated speed in feet per second, I the bow's IBO speed, l the draw length in inches, w the draw weight in pounds, a the arrow weight in grains and s the extra string weight in grains.

The result is then converted to metric using the exact definition 1 foot = 0.3048 metres.

Speed cannot go below zero. A very heavy arrow clamps the estimate at 0 fps rather than producing a negative number.

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):

$E = \frac{a \times v²}{450240}$

$p = \frac{a \times v}{225218}$

where E is the kinetic energy in foot-pounds, p the momentum in slug-feet per second, a the arrow weight in grains and v the speed in feet per second.

Both divisors are the constants archery references have long used. They come from the same physics: a grain is 1/7000 of a pound, and dividing a weight in pounds by gravity in ft/s² converts it to mass in slugs. Kinetic energy describes how much energy the arrow delivers on impact. Momentum describes how well the arrow keeps driving forward through resistance, such as hide and bone. Hunters often check both figures against the minimum recommended for the game they pursue.

Worked example

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

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 feet-lb of kinetic energy and about 0.447 slug·ft/s of momentum.

A bow shot at the exact IBO reference conditions returns the IBO number itself. With 70 pounds, a 30-inch draw, and a 350-grain arrow, the result is 320 fps, 97.5 m/s, 79.6 feet-lb of kinetic energy, and 0.497 slug·ft/s of momentum.

What the calculator accepts

IBO speed, draw weight, draw length, and arrow weight must each be greater than zero. Extra string weight may be zero but not negative. Every entry must be an ordinary finite number; a value too large to represent, such as one pasted into a shared link, is rejected rather than shown as a result. Leaving a field empty simply hides the result until it is filled in.

How accurate is this estimate?

The formula gives a working estimate, not a measurement. It ignores things that also change real arrow speed, such as bow efficiency, cam timing, temperature, string material, and friction at the arrow rest. A chronograph, a device that times an arrow as it passes two sensors, gives the true number for one specific bow and arrow. Archers commonly use the IBO estimate to compare setups or pick an arrow weight, then confirm the final figure on a chronograph.

Frequently asked questions

What does IBO speed mean? IBO speed is a bow's rated speed under a standard test: 70-pound draw weight, 30-inch draw length, and a 350-grain arrow. Manufacturers publish it so bows can be compared on equal terms.

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 slow the arrow below the IBO number. A draw length shorter than 30 inches lowers it further.

Does a heavier arrow always mean less kinetic energy? No. A heavier arrow flies slower, but kinetic energy depends on weight as well as speed. Over a moderate range, adding arrow weight can raise kinetic energy even as speed falls.

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 against resistance. Bowhunters read kinetic energy as overall power and momentum as penetration.

Can this calculator replace a chronograph? No. It applies standard adjustments to a published rating. A chronograph measures the real speed of one bow, arrow, and release, including effects the formula leaves out.

What happens if I enter a very heavy arrow? The estimate stops at zero. If the arrow weight adjustment would push the result below 0 fps, the calculator reports 0 fps instead of a negative speed.