Arrow Speed Calculator: Feet per Second & Kinetic Energy

This arrow speed calculator estimates the velocity of an arrow in feet per second (fps) based on your bow’s draw weight, draw length, arrow weight, and a few setup-specific factors. You enter your bow’s specifications and arrow mass, and the calculator returns the expected initial arrow speed and the kinetic energy it delivers at the shot. It uses a standard physics-based model that accounts for the energy stored in the bow and the efficiency of transferring that energy to the arrow.

Formula

The arrow speed is calculated from the energy stored in the bow and the arrow’s mass. The fundamental relationship is the kinetic energy equation:

KE = ½ × m × v²

Rearranged to solve for velocity:

v = √(2 × KE / m)

Where:

• KE = kinetic energy of the arrow (joules)
• m = mass of the arrow (kilograms)
• v = velocity of the arrow (meters per second)

In archery, the energy available to the arrow comes from the work done drawing the bow. A simplified model estimates this as:

KE = (Draw Weight × Draw Length) × Bow Efficiency

Here, draw weight is in pounds-force, draw length in inches, and bow efficiency is a decimal (e.g., 0.80 for 80%). This product gives the arrow’s kinetic energy in inch-pounds, which is then converted to joules. The calculator converts all inputs to SI units before applying the formula.

Worked Example

Using the default values from the calculator:

• Draw weight = 70 lb
• Draw length = 28 in
• Arrow weight = 400 grains
• Bow efficiency = 80%

First, convert to SI units:

• Draw weight in newtons: 70 lb × 0.454 kg/lb × 9.81 m/s² = 311.4 N
• Draw length in meters: 28 in × 0.0254 m/in = 0.7112 m
• Arrow mass in kilograms: 400 grains × 0.0000648 kg/grain = 0.02592 kg

Calculate the kinetic energy (work done by drawing the bow times efficiency):

KE = 311.4 N × 0.7112 m × 0.80 = 177.2 J

Now solve for velocity:

v = √(2 × 177.2 / 0.02592) = √(13680) = 116.95 m/s

Convert to feet per second: 116.95 m/s × 3.28084 = 383.7 fps

The calculator rounds to one decimal place, giving 383.7 fps.

Understanding Bow Efficiency

Bow efficiency is the percentage of the stored energy that actually transfers to the arrow. The rest is lost to heat, sound, and vibration in the bow limbs and string. Modern compound bows typically have efficiencies between 75% and 90%. Recurve bows are lower, often 65% to 80%. The efficiency depends on the bow design, string material, and how well the arrow’s spine matches the bow. If you don’t know your bow’s efficiency, a reasonable estimate is 80% for compound bows and 70% for recurves. The calculator lets you adjust this to match your specific setup.

How to Use the Calculator

To get the most accurate estimate, follow these steps:

1. Find your bow’s draw weight (in pounds) from the limb markings or a bow scale.
2. Measure your draw length (in inches) – the distance from the nock point to the deepest part of the grip plus 1.75 inches.
3. Weigh your arrow on a grain scale (or check the manufacturer’s spec).
4. Estimate your bow’s efficiency – use 80% for compounds, 70% for recurves, or consult your bow’s manual.
5. Enter these values into the calculator and read your estimated arrow speed and kinetic energy.

Common Mistakes and Limitations

The most common mistake is mixing units. Arrow weight is almost always given in grains, but some people enter ounces or grams. The calculator expects grains, so convert if needed (1 gram = 15.432 grains). Similarly, draw length must be in inches, not centimeters.

This model is a simplification. Real arrow speed is affected by many factors not captured here:

• Cam design (for compounds) – let-off and draw curve shape
• String material and number of strands
• Arrow spine and fletching drag
• Temperature (cold air is denser, slowing the arrow)
• Shooting elevation (air density changes with altitude)

The calculator gives a theoretical maximum under ideal conditions. Actual speeds are often 5-10% lower. For a more precise measurement, use a chronograph.

Why Arrow Speed Matters

Arrow speed directly affects trajectory and kinetic energy. Faster arrows fly flatter, meaning less holdover at longer distances. Kinetic energy (KE) determines penetration – the ability to drive the broadhead through game. The calculator shows both speed and KE, so you can see the trade-off: a heavier arrow has less speed but more KE (since KE scales with mass, but only with the square of velocity). Hunters often prefer heavier arrows for deeper penetration, while target shooters favor lighter arrows for flatter trajectories.

For example, a 70 lb bow with a 400-grain arrow at 383 fps delivers about 130 ft-lb of KE. Dropping to a 350-grain arrow might give 410 fps but only 125 ft-lb. The heavier arrow actually retains more energy downrange because it’s less affected by air resistance.

Frequently Asked Questions

How accurate is this arrow speed calculator?

It’s a close estimate, typically within 5-10% of actual speed. The main uncertainty is bow efficiency, which varies with your specific setup. For exact numbers, use a chronograph or ballistic chronograph.

What is a good arrow speed for hunting?

Most hunters aim for 280-320 fps. This gives a reasonably flat trajectory while allowing a heavy enough arrow for good penetration. Faster is not always better – very light arrows may not penetrate deeply on large game.

How does arrow weight affect speed?

Arrow speed is inversely proportional to the square root of arrow mass. Doubling the arrow weight reduces speed by about 29% (1/√2). But kinetic energy actually increases by about 41% because the mass increase outweighs the speed loss.

What is the difference between IBO speed and actual speed?

IBO speed is a standardized rating: a bow’s speed with a 350-grain arrow, 30-inch draw length, and 70-pound draw weight. Real-world setups rarely match these exact conditions, so actual speed is usually lower. This calculator uses your actual inputs, not IBO standards.

Can I use this calculator for crossbows?

Yes, but with caution. Crossbows have a much shorter power stroke (draw length) and different efficiency. The formula still applies, but you need accurate values for draw length and efficiency. Many crossbows have published speed ratings that you can compare against.

Does arrow spine affect speed?

Arrow spine (stiffness) doesn’t directly change speed, but a mismatched spine can cause poor flight, which reduces effective speed due to drag and oscillation. A properly spined arrow will fly faster and more accurately than one that’s too stiff or too weak.

Safety Considerations

When testing arrow speed, always use a proper backstop and never dry-fire a bow (shooting without an arrow). Dry-firing can damage the bow and cause injury. When using a chronograph, set it up at a safe distance and follow the manufacturer’s instructions. Always wear eye protection and be aware of your surroundings. Arrow speed is a useful metric, but safety should always come first.

Related

• Active Pace Calculator: Running Pace and Speed
• 4L80E Gear Ratio Calculator and Transmission Specs
• Bowling Rev Rate: How to Calculate Your RPM

in dw | Draw weight | lb | 70 | 0
in dl | Draw length | in | 28 | 0
in aw | Arrow weight | grains | 400 | 0
in bw | Bow efficiency | % | 80 | 0
out speed | Arrow speed | fps | sqrt(2 * (dw * 0.454 * 9.81) * (dl * 0.0254) * (bw / 100) / (aw * 0.0000648)) | 1
out ke | Kinetic energy | ft-lb | (aw * 0.0000648) * (speed * 0.3048)^2 / 2 / 0.73756 | 1