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 Hunted	Kinetic 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 Goldtip.com

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 Hunted	Momentum 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.

Hunting Arrow Setups & Related Posts

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)
398	269	63.94	0.475
423	261	63.97	0.490
448	252	63.16	0.501
473	244	62.52	0.512
498	236	61.58	0.522
523	227	59.83	0.527
548	219	58.35	0.533
573	211	56.64	0.537
598	202	54.17	0.537
623	194	52.05	0.537
648	186	49.77	0.535

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

What are the factors that affect arrow speed when shooting a compound bow?

When shooting a compound bow, several factors affect the speed at which an arrow flies:

1. Draw Weight: The amount of draw weight you pull influences arrow speed. Higher draw weight results in faster arrow velocity. Typically, for every 10 lbs. of draw weight reduction, the arrow speed decreases by 15-20 feet per second (fps).

2. Draw Length: The length of your draw impacts arrow speed. Longer draw lengths create a longer power stroke, allowing the bow to store more energy and increasing arrow speed. As a general guideline, for every additional inch of draw length, arrow speed can increase by approximately 10-15 fps.

3. Arrow Weight: The weight of the arrow itself affects its speed. Adding more weight to the arrow will reduce its speed. On average, for every 5 grains of added arrow weight, the raw speed of the arrow decreases by 1-2 fps.

4. Bowstring Weight: The weight added to the bowstring, such as peep sight, string silencers, or string loop, can also impact arrow speed. Increasing the weight by around 20 grains may lead to a deduction of about 5 fps from the raw arrow speed.

What is the significance of shooting a hunting arrow through a chronograph to determine its actual speed?

Shooting a hunting arrow through a chronograph is crucial in accurately determining its actual speed because while an arrow speed calculator can provide an estimate, shooting the arrow through a chronograph provides precise data on the speed at which it is flying.

This direct measurement eliminates any uncertainty or potential inaccuracies that may arise from relying solely on calculated estimates. Therefore, using a chronograph ensures that hunters have an exact understanding of how fast their arrows are moving, allowing for better fine-tuning of equipment and improved performance in the field.

How is kinetic energy defined and how is it related to arrow shafts?

Kinetic energy is a concept rooted in the idea of motion and active work, derived from the Greek terms for motion and active work. It represents the energy associated with the motion of an object. In the context of arrow shafts, kinetic energy plays a crucial role in determining their penetrating ability.

When a bow is drawn, energy is stored in its limbs and cams, which is then transferred to the arrow shaft upon release. This transfer of energy manifests as kinetic energy, denoted as K.E. The speed of the arrow shaft decreases during flight due to factors such as gravity and air resistance, causing changes in the kinetic energy along its trajectory.

Thus, kinetic energy is instrumental in understanding how efficiently arrow shafts can penetrate their target.

Why is finding the right balance between arrow speed and weight crucial for optimizing penetration power in bowhunting?

The balance between arrow speed and weight is crucial because it determines the penetration potential of hunting arrows. While kinetic energy favors speed and momentum favors weight, finding the optimal combination is essential to ensure effective penetration and lethality when hunting larger or tougher animals.

What are the implications of adjusting kinetic energy and momentum for arrow lethality and penetration potential in bowhunting?

Adjusting kinetic energy and momentum can impact the lethality and penetration potential of hunting arrows. Finding the sweet spot between arrow speed and weight is crucial for optimizing penetration power, as heavier arrows tend to penetrate better but may sacrifice speed, while lighter arrows may offer increased speed but potentially reduce momentum.

How do arrow speed, arrow weight, and other factors impact kinetic energy and momentum for hunting arrows?

Arrow speed and weight directly affect kinetic energy, with velocity playing a significant role in K.E. Calculations. Momentum, on the other hand, is influenced by both mass and velocity, highlighting the importance of finding the right balance between arrow speed and weight for optimal penetration power.

What is the relationship between kinetic energy and momentum in the context of bowhunting?

Kinetic energy is likened to a driving force (hammer) that propels the arrow through the animal, while momentum is described as energy retention downrange or penetration potential. Kinetic energy favors arrow speed due to velocity squared, while momentum gives equal importance to mass and velocity.

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