Welcome to our Arrow Speed, Kinetic Energy, and Momentum Calculator, where you can easily calculate your arrow’s speed, kinetic energy, and momentum based on the IBO speed of your compound bow, your draw weight, draw length, and arrow weight. As you know, IBO speed is a standard measure of the speed of a bow, and by using it as a baseline for all calculations, our calculator can provide you with accurate and reliable results. Keep reading to learn how to use our calculator and how to optimize your arrow for your hunting needs.
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. The combined speed, kinetic energy, and momentum calculator below will help you estimate the potential each arrow has based on its weight and your personal bow setup and settings.
*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.
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 is traveling 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
- 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 per second 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 a 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.
For example, it takes approximately 40 ft/lbs(+or-) of kinetic energy to kill a whitetail deer. When you input your bow and arrow’s information in the calculator below, you can see right away what your arrow’s potential is. One thing to remember is that while kinetic energy provides the impact of your arrow on your intended target, what it doesn’t necessarily provide is information on your arrow’s ability to penetrate and travel through your target. That is defined by an arrow’s weight, broadhead, and momentum.
| 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 |
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 |
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.
See our List of Archery Calculators below:
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.
The values in the table below come from the following bow and its associated settings.
- 2022 Bear Alaskan Right-Handed 55-70 lb Model
- Draw Length – 27″
- Draw Weight – 62 lbs
- Arrow Weight – 423 grains (Easton Axis 5mm Arrows) – *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 |
If you change the values on your draw weight, draw length, and arrow weight; you will see how these changes impact your arrow speed, kinetic energy, and momentum. You can also see how increasing your arrow weight will increase kinetic energy and momentum, but then decrease kinetic energy when the speed of your arrow decreases to the point where it can no longer provide the force necessary to increase your arrow’s lethality.
Using the calculator above, you can see how changing even the smallest things can affect the lethality of your hunting arrows. Use this tool to optimize your arrows now.
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