Arrow Speed & Kinetic Energy Calculator

This calculator works out the speed and kinetic energy of an arrow from its mass and velocity. You enter the arrow’s mass in grains and its speed in feet per second, and you get back the speed in feet per second (if you entered it) and the kinetic energy in foot-pounds, plus the momentum in slug-feet per second. The kinetic energy figure is the one most archers use to compare bow setups and estimate hunting capability.

Formula

The kinetic energy of an arrow is calculated with the standard physics equation:

KE = ½ × m × v²

where:

• KE = kinetic energy in foot-pounds (ft-lb)
• m = arrow mass in slugs (pounds-mass divided by the acceleration of gravity, 32.174 ft/s²)
• v = arrow speed in feet per second (fps)

Because arrow mass is commonly given in grains, the formula converts grains to pounds (1 lb = 7000 grains) and then to slugs by dividing by 32.174. The constant 64.348 in the calculator is simply 2 × 32.174, which combines the ½ and the gravity conversion.

Worked Example

Using the default values from the calculator: arrow mass = 400 grains, arrow speed = 300 fps.

1. Convert mass to pounds: 400 / 7000 = 0.05714 lb
2. Convert pounds to slugs: 0.05714 / 32.174 = 0.001776 slugs
3. Square the speed: 300² = 90,000
4. Apply the formula: KE = ½ × 0.001776 × 90,000 = 79.9 ft-lb

The calculator rounds to one decimal place, so it shows 79.9 ft-lb. The momentum is (0.05714 / 32.174) × 300 = 0.53 slug-ft/s.

Why Kinetic Energy Matters for Arrows

Kinetic energy tells you how much work the arrow can do on impact. A heavier arrow moving slower can have the same kinetic energy as a lighter arrow moving faster, but the two will behave differently on target. Higher kinetic energy generally means deeper penetration on game, assuming the arrow and broadhead are designed to hold together. For target shooting, kinetic energy is less important than arrow flight and consistency, but it still affects how much noise the bow makes and how the arrow reacts to wind.

Momentum is a separate but related quantity. It is the product of mass and velocity, and it describes how hard the arrow is to stop. Two arrows with the same kinetic energy can have different momentum. The one with more momentum (heavier and slower) tends to push through resistance better, which is why some hunters prefer heavy arrows even if they lose speed.

How to Measure Arrow Speed

You cannot calculate kinetic energy without knowing the arrow speed. The standard tool is a chronograph, which measures the time it takes the arrow to pass two sensors a known distance apart. Most modern chronographs are optical and display speed in feet per second. You can also estimate speed from the bow’s advertised IBO rating, but that rating is measured with a specific setup (usually 70 lb draw weight, 30-inch draw length, and a 350-grain arrow) and will not match your actual bow. The only reliable way is to shoot your own arrow through a chronograph.

Arrow speed depends on several factors:

• Draw weight and draw length of the bow
• Arrow mass (heavier arrows are slower)
• String material and weight
• Cam design (for compound bows)
• Fletching and nock weight

Choosing Arrow Mass for Your Goal

There is no single “best� arrow weight. It depends on what you are doing:

• Target archery: Lighter arrows (around 5–6 grains per pound of draw weight) fly flatter and faster, which helps with distance judging and wind drift.
• Hunting small game: A medium arrow (6–8 grains per pound) gives a good balance of speed and penetration.
• Hunting large game: Heavier arrows (8–10 grains per pound) carry more momentum and penetrate better, especially on tough animals like elk or moose.

A common rule of thumb is to use at least 5 grains of arrow mass per pound of draw weight for target shooting, and 6–8 grains for hunting. But the kinetic energy calculator lets you compare specific setups: if you know your bow’s speed at a given arrow weight, you can see how much energy you gain or lose by changing arrow mass.

Common Mistakes and Misconceptions

One frequent error is mixing units. If you enter arrow mass in grams instead of grains, the result will be off by a factor of about 15.4. Another mistake is using the bow’s advertised speed (IBO rating) without adjusting for your actual draw length and arrow weight. The IBO speed is measured with a 350-grain arrow, so your real arrow will almost always be slower.

A common misconception is that a faster arrow always penetrates better. That is not true. Penetration depends on kinetic energy, but also on arrow diameter, broadhead design, and the target material. A heavy, slow arrow can penetrate deeper than a light, fast one if it retains more energy on impact. Also, kinetic energy is not the same as “knockdown power� – no arrow reliably knocks an animal over. The goal is a clean pass-through, which requires sufficient energy and good shot placement.

Limits of the Kinetic Energy Formula

The formula KE = ½mv² assumes the arrow is a rigid body moving in a vacuum. In reality, arrows flex (archer’s paradox) and lose speed to air drag. The kinetic energy you calculate from the initial speed is the maximum energy available at the bow; by the time the arrow reaches the target, it has lost some speed to drag. The loss is small at typical archery ranges (under 60 yards) but becomes significant at longer distances. For most hunting and target situations, the initial kinetic energy is a good practical measure.

The formula also does not account for the energy lost to the bow itself (efficiency) or the energy stored in the limbs. It only describes the arrow after it leaves the bow. If you want to compare bows, you need to measure the actual arrow speed, not just the bow’s draw weight.

Cost and Equipment Considerations

You do not need any special equipment to use this calculator, but to get the arrow speed you will need a chronograph, which typically costs between $50 and $150. Some archery shops have one and will let you shoot through it for a small fee or for free. Arrow scales that measure in grains are also useful, since arrow weight can vary by a few grains depending on inserts, points, and fletching. A digital grain scale costs around $20–$40.

If you are buying arrows, the weight is usually listed on the shaft (e.g., 8.5 grains per inch) but the total arrow weight includes the point, insert, nock, and fletching. Weighing the complete arrow is the most accurate.

Frequently Asked Questions

What is a good kinetic energy for bowhunting?

There is no universal number because it depends on the animal and the arrow setup. Many hunters consider 25–40 ft-lb adequate for whitetail deer with a well-tuned bow and a sharp broadhead. For larger game like elk, 50–65 ft-lb is often recommended. These are general guidelines, not guarantees – shot placement and arrow construction matter just as much.

How do I convert grain to grams?

One grain equals 0.0648 grams. To convert grams to grains, divide by 0.0648 or multiply by 15.43. For example, a 400-grain arrow is about 25.9 grams. The calculator uses grains directly, so you do not need to convert unless your scale reads in grams.

Does arrow speed decrease with distance?

Yes, due to air drag. A typical arrow loses about 1–2 fps per 10 yards, depending on the arrow’s shape, fletching, and speed. At 60 yards, you might lose 6–12 fps. The kinetic energy at the target is lower than what the calculator shows, but the difference is usually small enough that hunters still use the initial speed for planning.

What is the difference between kinetic energy and momentum?

Kinetic energy is the energy of motion and depends on the square of speed, so speed matters more. Momentum is the product of mass and speed and is a measure of how hard it is to stop the arrow. For penetration, momentum is often a better predictor because it accounts for the arrow’s ability to push through tissue. The calculator shows both so you can compare.

Can I use this calculator for crossbow bolts?

Yes. Crossbow bolts are arrows, just shorter and often heavier. The physics is identical. Enter the bolt’s mass in grains and its speed in fps, and you will get the correct kinetic energy and momentum.

Why does my bow’s advertised speed not match my chronograph?

Manufacturers measure IBO speed under specific conditions: 70 lb draw weight, 30-inch draw length, and a 350-grain arrow. Your bow likely has a different draw weight, draw length, or arrow weight, all of which change speed. Also, the string, cables, and cam condition affect speed. The advertised number is a maximum, not a guarantee.

Related

• Pressure Altitude Calculator: Formula and Examples
• Recoil Energy Calculator: Formula and Example
• Calculating Power in Physics: Formula and Examples

in m | Arrow mass | grains | 400 | 0
in v | Arrow speed | fps | 300 | 0
out ke | Kinetic energy | ft-lb | (m / 7000) * (v^2) / 64.348 | 1
out mom | Momentum | slug-ft/s | (m / 7000) * v / 32.174 | 2