Arrow Speed Calculator

Arrow Speed Calculator estimates how fast an arrow leaves a bow from its IBO rating, draw length, draw weight and arrow weight. It also gives its kinetic energy, momentum and drop.

Arrow Speed Calculator Formula

A bow’s printed speed is measured under test conditions that few archers shoot. The Arrow Speed Calculator corrects that rating for your draw length, your arrow and the weight on your string. It uses the rule of thumb published by bowhunting sources such as N1 Outdoors.

$$v = v_{IBO} + 10 (L – 30) – \frac{W – 5D}{3} – \frac{S}{3}$$

Each inch of draw under 30 in costs 10 fps. Every 3 grains of arrow weight above 5 grains per pound of draw costs 1 fps, and so does every 3 grains on the string. The arrow term only applies when the arrow is heavier than 5 times the draw weight, and it changes form for very heavy arrows, as shown further down.

The default entries are a 340 fps bow at 28.5 in and 65 lb with a 400 grain arrow and a 20 grain peep. Draw length takes off 15 fps. The arrow is 75 grains over the 325 grain baseline, which takes off 25 fps. The peep takes off about 7 fps. The estimate is 293 fps.

What an IBO Rating Means

A speed rating is shot at a 30 in draw length with an arrow of 5 grains per pound of draw weight. The ATA method fixes the bow at 70 lb, so the arrow weighs 350 grains. The IBO method allows up to 80 lb with a 400 grain arrow. Evan Williams sets out both in Rokslide’s article on ATA and IBO bow speed.

The string is bare during the test, with no peep or silencers. Almost every hunting setup has a shorter draw, a heavier arrow and a loaded string, so real speed comes out lower. Darron McDougal works one case in Grand View Outdoors.

A 340 fps bow at 29 in and 60 lb with a peep, two silencers and a 400 grain arrow lands at 280 to 290 fps. The Arrow Speed Calculator returns 282 to 290 fps for that setup with 20 to 45 grains on the string.

Draw weight itself matters far less. Mossy Oak’s guide puts a bow at 60 lb only 3 to 4 fps under its 70 lb speed when the arrow stays at 5 grains per pound. That is why the formula has no separate draw weight term.

The rating itself can be optimistic. The Ashby Bowhunting Foundation warns that most IBO ratings are not real-world numbers and that some bows are significantly off. The Arrow Speed Calculator shows how far your setup sits from the rating and splits the loss between draw length and weight.

Correct the Rating With a Chronograph

A chronograph reading beats any estimate. Switch What You Know to Chronograph reading, then enter the measured speed and the setup it was shot with. The Arrow Speed Calculator works back to the rating the bow really behaves like.

That figure can then be used to try other arrows. The reverse step uses the same heavy-arrow handling, so a reading taken with a 650 grain arrow still returns the right rating.

Ashby gives a worked case. A 70 lb, 29 in bow rated at 350 fps was measured at 315 fps with a 400 grain arrow. With a 20 grain peep on the string, the formula above predicts 317 fps for that bow, 2 fps from the measured speed. Run in reverse, the same reading gives a true rating of 348 fps, where Ashby’s own method gives 346 fps.

Kinetic Energy and Momentum of an Arrow

Kinetic energy is half the mass times the speed squared. Archery uses a shortcut that takes arrow weight in grains and speed in fps and returns foot-pounds. The divisor folds in the 7,000 grains in a pound and twice the standard acceleration of gravity, 32.174 ft/s². Archery sources usually print 450,240, which differs by 0.04%.

$$KE = \frac{1}{2} m v^2$$

$$KE = \frac{W v^2}{450437}$$

The 400 grain arrow at 293 fps carries 76.4 ft-lb, or 103.6 J. Deer and Deer Hunting magazine lists the energy levels long used as minimums for game, in its article on kinetic energy and momentum.

Momentum is mass times speed. It favors a heavy arrow more than energy does, and the same article describes it as penetration potential. With weight in grains and speed in fps, the result is in slug-feet per second. Bow makers such as EK Archery publish the same momentum constant.

$$p = \frac{W v}{225218}$$

The example arrow has 0.521 slug-ft/s, which is 2.32 kg·m/s. The same card gives arrow weight per pound of draw. At 400 grains on a 65 lb bow that is 6.2 grains per pound. An arrow under 5 grains per pound triggers a warning, because bow makers set a minimum arrow weight.

Heavy Arrows and the 3 Grain Rule

Used alone, the 3 grain rule takes off 1 fps for every 3 grains however heavy the arrow gets. Past a certain weight that makes the arrow’s energy fall, and a real bow does not behave that way. Ashby notes that bows gain efficiency as arrow weight rises.

The Arrow Speed Calculator follows the rule up to the weight where the rule’s own energy peaks. That happens when the speed in fps equals two-thirds of the arrow weight in grains. For the default bow it is 427 grains at 284 fps, about 6.6 grains per pound. Past that weight the energy is held steady and speed falls with the square root of the weight.

$$v_2 = v_1 \sqrt{\frac{W_1}{W_2}}$$

At 650 grains the rule alone would give 210 fps and only 63.6 ft-lb. The calculator gives 230 fps and keeps the full 76.6 ft-lb, while momentum keeps climbing. The estimate is still on the low side for a heavy arrow, because a real bow gains a little energy where the calculator only stops losing it. A chronograph reading settles it.

Arrow Drop and Flight Time

For drop, the Arrow Speed Calculator treats the arrow as a projectile with no air drag. Flight time is the distance divided by the speed. Drop is the fall under gravity in that time, measured below the line the arrow left the bow on.

$$t = \frac{d}{v}$$

$$y = \frac{1}{2} g t^2$$

The last column is why speed matters to a hunter. It is how low the arrow lands when the target is 5 yd farther than judged. A 250 fps arrow drops 25.0 in at 30 yd, against 18.2 in at 293 fps. Real arrows slow in flight, so true drop at long range is a little more than these figures.

Arrow Speed in m/s and km/h

The headline restates every result in other units. The 293 fps example is 89.4 m/s, 200 mph and 322 km/h. The Units list switches the Arrow Speed Calculator to meters for distance, to m/s for speed, or to a full metric set with centimeters, kilograms and grams. Energy then reads in joules and momentum in kg·m/s.

Recurve Bows and Crossbows

The correction rule was built for compound bows, which are the bows that carry an IBO rating. A recurve or longbow has no such rating. Crossbows have no shared test at all, and TenPoint notes that makers usually advertise the speed of their lightest arrow. Used as a recurve or crossbow arrow speed calculator, the tool needs a measured speed, so pick the chronograph option.

The measured speed then drives the energy, momentum, drop and flight time. Those are plain physics and apply to any arrow or bolt. Other motion tools are listed on the Kinematics Calculators page.