Arrow Speed, Kinetic Energy, and Momentum Calculator

Arrow Speed, Kinetic Energy, and Momentum Calculator

If you need to find what your arrow speed, kinetic energy, and momentum are, then the calculator below will give you the results you need fast. No need to do any math, but if you want, the formulas are here too.

Many bowhunters buy arrows that fit their bow, their draw weight, and their draw length; but fail to understand the unique characteristics of each arrow and the arrow’s ability to penetrate and kill the wild game they are hunting.

Get started by using the arrow calculator below now.

*NOTE: The calculator below will provide you with an estimate based on your inputs. The only way to find the exact speed of your specific arrow is with an arrow chronograph. This tool should get you close to that.

Testing arrow penetration after using the arrow speed, kinetic energy, and momentum calculator.

Arrow Speed Factors

When an arrow is shot from your bow, its impact, and ability to penetrate and make the kill is based not just on the speed of your bow. There are a few more things that impact how fast your arrow travels after you shoot.

The factors that impact the overall speed of your arrow are:

  • The IBO-rated speed of your bow
  • Your bow’s set draw length
  • Your bow’s draw weight
  • Your arrow’s total weight – See Why This Matters
  • Any additional weight on your bowstring (nock loop, peep, etc.)

Rules of Thumb

In addition, it is important to understand that sometimes even minor changes to your draw length, draw weight, and arrow weight can seriously affect the speed, kinetic energy, and momentum of your arrows when they are shot from your bow.

Here are a few rules of thumb to remember:

  • For every inch of draw length under 30″, subtract 10 feet per second (fps) from the IBO-rated speed value.
  • For every inch of draw length above 30″, add 10 fps to the IBO value.
  • For every 3 grains of total arrow weight above draw weight multiplied by 5, subtract 1 fps from the IBO value.
  • For every 3 grains of additional weight on the bowstring, subtract 1 fps from the IBO value.

Gravitational Constant

The Kinetic Energy and Momentum Calculators here use the gravitational constant to give you the best results for kinetic energy and momentum. Factoring in the gravitational constant in both of those formulas for hunting arrows is necessary to account for the effect of gravity on the arrow’s motion.

The gravitational constant (g) is the acceleration due to gravity, which is 32.174 feet per second squared at sea level.

Arrow Speed Calculator

Arrow speed is determined by your bow’s IBO speed (fps), your draw weight (in pounds lbs)), your draw length (in inches), the arrow’s total weight (in grains), and the weight of what is on the bowstring (in grains) as outlined above. Remember, the speed of your arrow is at the point of the shot. The speed decreases exponentially as the arrow travels.

The speed of your arrow will determine how flat of a trajectory your arrow has at short and long distances and how much arc is needed to travel large distances. Speed is needed to make the arrow arrive at its target quickly, but arrow speed is not what kills the animals you shoot with your bow.

What allows an arrow to ethically and effectively kill wild game is the right combination of kinetic energy and momentum.

Arrow Speed Formula

To properly calculate arrow speed, use the following formula:

IBO Speed(in fps) + (Draw Length – 30) x 10 – Additional Weight on Bowstring (in grains) / 3 + MIN(0, – (Arrow Weight(in grains) – 5 x Draw Weight in Pounds) / 3 ))

Arrow Kinetic Energy Calculator

Kinetic energy (KE) is a measure of an arrow’s ability to transfer energy upon impact, and a higher KE can result in greater penetration and stopping power. A 10 ft-lbs difference in KE can potentially result in a noticeable difference in the arrow’s ability to effectively penetrate the animal and cause a humane kill.

In hunting game of varying sizes, minimum kinetic energy values have been recommended to ensure effective and ethical hunting practices. For small game such as rabbits and squirrels, it is advisable to use an arrow that delivers up to 25 ft./lbs. of kinetic energy.

Medium-sized game like deer, pronghorn, and sheep require an arrow with a kinetic energy range of 25-41 ft./lbs. When hunting large-sized game such as elk, black bear, and wild boar, it is recommended to have ammunition with a kinetic energy range of 42-65 ft./lbs.

For the toughest game including brown bear, grizzly bear, and large African game, a minimum of 66 ft./lbs. or more of kinetic energy is advised for effective and humane hunting outcomes.

Wild Game HuntedKinetic Energy Required (estimated)
Small Game (rabbit, groundhog, etc.)< 25 ft. lbs
Medium Game (deer, antelope, etc.)25-41 ft. lbs
Large Game (elk, black bear, wild boar, etc.)42-65 ft. lbs
Toughest Game (cape buffalo, grizzly, musk ox, etc.)> 65 ft. lbs
Courtesy of

The KE Formula

To correctly calculate kinetic energy, use the following formula:

1/2 Mass (Arrow Weight in grains divided by 2) x Velocity squared (Arrow Speed x Arrow Speed (in fps from the above formula)) / 225218 – The result of this formula is calculated in foot-pounds (ft-lbs).

Arrow Momentum Calculator

While KE is an important factor in penetration, momentum is also critical because it determines the arrow’s ability to push through the target. Momentum is often considered more important for hunting because it can help the arrow maintain its penetration potential.

An arrow’s momentum is defined by how much force is required to stop an object. In other words, how much force is required to stop an arrow? How far will it penetrate? In the calculator below, we measure this in slugs.

The table below provides us with a general idea of how much momentum is needed for different types of wild game and it also shows us the arrow’s penetration capability when coupled with KE. When you look at this and compare it to the table above, you can calculate what the right arrow can accomplish after you shoot it.

Wild Game HuntedMomentum Required (estimated)
Small Game (rabbit, groundhog, etc.)0.163-0.210 slug fps
Medium Game (deer, antelope, etc.)0.207-0.305 slug fps
Large Game (elk, black bear, wild boar, etc.)0.349-0.433 slug fps
Toughest Game (cape buffalo, grizzly, musk ox, etc.)0.481-0.532 slug fps
Courtesy of GritOutdoors

The Momentum Formula

To properly calculate momentum, use the following formula:

Mass (Arrow Weight in grains) x Velocity (Arrow Speed (in fps)) / 225218 – The result of this formula is calculated in slugs.

*Slugs can be converted to Pound-Seconds by multiplying the result from the above formula by 32.174. 1 slug equals 32.174 ft-lbs.

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Using the Arrow Speed, Kinetic Energy, and Momentum Calculator

When using the calculator above, input your values and then compare them to those values in the tables below. You will find that most modern bows are more than capable of killing most game animals. What is important, is understanding how this impacts the arrow you choose to buy and use when hunting, along with the broadheads you use.

In the table below, you will see some base values there already, they are there to show you an example of a real-world situation with real values and what they look like when compared to a mid-range bow and mid-range set of arrows.

A lighter arrow produces more arrow speed, but an increase in arrow weight (incremented by 25 grains) can increase and eventually decrease arrow kinetic energy. A heavy arrow will produce a great deal of arrow momentum even at the price of arrow speed, but will eventually go down as arrow speed decreases.

Heavy arrows, coupled with the right speed for your target animal, optimized by a high FOC, can accomplish a lot more than a light, fast arrow.

READ: What is the Best Hunting Arrow Weight (For You)?

The values in the table below come from the following bow and its associated settings.

  • 2022 Bear Alaskan Right-Handed 55-70 lb Model – 335 fps IBO Speed
  • Draw Length – 27″
  • Draw Weight – 62 lbs
  • Arrow Weight – 423 grains *includes a 125-grain broadhead
  • Additional Weight on Bowstring – 20 grains
Arrow Weight (grains)Arrow Speed (fps)Kinetic Energy(ft-lbs.)Momentum (slug)
Table Measurements based on a 25-grain increase in Arrow Weight and the 2022 Bear Alaskan Compound Bow and the settings listed above this Table.

If you change the values on your draw weight, draw length, and arrow weight; you will see how these changes impact your arrow’s speed, kinetic energy, and momentum’s effectiveness.

It becomes evident that increasing arrow weight enhances kinetic energy and momentum, although it leads to a decline in kinetic energy as arrow speed decreases to the point where it no longer delivers the force needed to enhance the lethality of your arrow.

Using the arrow speed, kinetic energy, and momentum calculator above, you can see how changing even the smallest things can affect the lethality of your hunting arrows. Once you are done and have your arrows, don’t forget to use paper tuning to optimize your arrows for optimal results.

Frequently Asked Questions

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