Formulas and tech Details

Kinetic Energy vs. Momentum

I have read and studied this subject referencing many different sources. It is confusing at best. The terms Kinetic Energy and Momentum, while different are used simultaneously and interchangeably to describe the energy of the bow and arrow. The explanation you will get on this site is an over simplification or synopsis of the subject. For an in-depth technical discussion please refer to the recommended readings listed below.


Kinetic energy is really a measurement of the total energy an arrow and broadhead develop at a given moment of time while being delivered by a particular bow. The reason the measurement is only at a particular moment is that as soon as the arrow is released, and until it hits the intended target, it is continually losing speed. As the velocity decreases so will the Kinetic energy. This reinforces the assertion that KE is a measurement of energy for the bow as this will be the place of the highest KE measurement and the lowest measurement will be at the target.
The KE measurement is a useful measurement when comparing different arrow and broadhead combinations shot from the same bow or determining how much energy a bow creates. It is not a practical measurement to determine what effect the arrow will have in penetrating an animal. Some archers swear by KE and believe that only a bow delivering a certain amount of KE should be used for hunting purpose. This is contrary to what the KE formula tells us.


The kinetic energy formula is:

        “1/2 Mass times velocity squared” or “KE = (1/2 M) x (V2)”


For your convenience use the inter-active formula below to calculate KE


Analyzing this we see that a small increase in velocity moves KE up quickly. It is hard to increase KE without increasing the velocity of the arrow. Using mechanical bows one can use special cams, overdraw systems and lighter arrows to increase velocity Light arrows and speed do not necessarily lead to killing power. Throw a child’s plastic baseball as hard as you can and then repeat the process with a regular baseball. It is obvious that the lighter, ball which may travel faster at first will lose energy faster and does less damage on impact than the slower and heavier of the two. The results of the ball experiment can easily be transferred to an arrow. The heavy arrow traveling at a relative slow speed will have more killing power than a light arrow traveling at high speed.


If one studies KE and momentum they would conclude that momentum formula results are more meaningful to the bowhunter as momentum can be translated into penetration potential. “Momentum is the measurement of concentrated force that is moving in one specific direction over a period of time.” The key words here are ”direction and period of time” Momentum measurement of energy is based on the weight and speed of the arrow that is available for impact and penetration. With this in mind we should consider Momentum.


 The formula for momentum calculation is:
        “Momentum = mass multiplied by velocity or p = (m)x(v)”

(Note: You ask why P stands for momentum? “The symbol P for momentum comes from the original term used to describe persistence of the object's motion” )


The term “Persistence” describes how we want our arrow and broadhead to perform. Momentum or Persistence is what drives the arrow and broadhead into the animal. Momentum being the combination of arrow weight and velocity is what propels the arrow through the hide, tissue and bone. This is why Momentum is more meaningful to the bowhunter than Kinetic Energy. Going back to the formula for momentum we see that velocity plays a part but is not more significant than mass. From this we can conclude that if the velocity is kept constant and the weight of the arrow is increased the momentum (P) of the arrow is increased proportionally. This is good news particularly for the traditional archer. The traditional archer can concentrate on arrow mass which is easily controlled or varied rather than on velocity which generally can only be increased by shooting heavier draw weight bows. By increasing arrow weight or mass we can see a significant increase in Momentum (Persistence) and increased penetration potential. This opens up a new world in arrow design. We can study and experiment with “forward of center arrows” (FOC),”extreme forward of center arrows” (EFOC) and “ultra extreme forward of center arrows”(Ultra-EFOC).Remember the ball analogy; the heavier baseball does more damage on impact. The heavier slower arrow has more momentum (P) than the lighter arrow, and thus does more damage on impact and has persistence to penetrate. Summing up, calculations of KE for a light fast arrow may indicate high kinetic energy (KE) but will have a relatively low momentum (P) compared to a heavier arrow traveling at a slower speed.


Momentum (P) and Kinetic Energy (KE) along with weight forward of center arrows (WFOC) are being considered by more and more archers as they become educated and convinced that arrow speed alone does not kill!


Other discussions of Momentum and Kinetic Energy can be found at the following sites:

KE is not Momentum, Nov 21, 2007 ... Beginning students often confuse kinetic energy and momentum. ... Consider the momentum and kinetic energy of the truck and the meatball

How a Traditional Bow Kills, Oct 22, 2008 Africa's Bowhunter Magazine... So what would be the better way to describe an arrow's performance, kinetic energy or momentum?  ….

Momentum and KE, by Dr. Ed Ashby

Try this out.

Enter both the weight and velocity values and hit the Calculate button.

Try different values and see what effect arrow wieght and velocity have on Momentum.

Kinetic Energy / Momentum Calculator

Enter Arrow Weight AND Arrow Velocity then press the "Calculate" button:

Arrow Weight (grains)

Arrow Velocity

Kinetic Energy

(Slugs or lb.ft.-sec)

   Made in the USA