Arrow Speed Calculator

This archery speed calculator estimates the speed at which an arrow leaves a bow based on equipment values. It uses your bow specs as a starting point and takes into account draw length, draw weight, arrow weight, and any accessories attached to the string. The speed is then converted into two values that are particularly important for hunters: kinetic energy and momentum.

What is meant by arrow speed?

Arrow speed is the velocity at which an arrow leaves the bowstring. It affects how flat the flight path of the arrow is, the distance between target points on a sight and the time it takes for the arrow to reach its target. A higher speed does not necessarily mean better performance. Lighter arrows fly faster but have less energy. Heavier arrows are slower but have more penetrating power and cause a greater impact upon hitting their target.

IBO and ATA speed ratings

Manufacturers list speeds so buyers can compare different models. The IBO rating is set by the International Bowhunting Association and measures under specific conditions: 30 inches of draw length, 70 pounds of draw weight, and a 350-grain arrow. This equates to 5 grains per pound of draw weight. The ATA rating from the Archery Trade Association uses a similar test but with slightly heavier arrows. Both ratings are for ideal lab conditions so actual speeds will usually be lower.

This is how to use this calculator.

Select the mode at top. In the Estimate Mode enter your bow's IBO or ATA rating, draw length, draw weight, finished arrows' weight and any additional weights attached to the bow (e.g., peep sight, D-Ring, dampener). The calculator will output estimated speed as well as kinetic energy, momentum, and grain per pound.

If you have a chronograph, switch it to measuring mode and input the measured values. The calculator will then calculate the energy, momentum, and grain per pound using the actual velocity. This is the most accurate method of obtaining these values.

Formula for calculating arrow speed:

This estimate makes four simple adjustments to the rated speed.

• An increase of 10fps is made when the draw length is over 30 inches. Below that it reduces by 10fps per inch.

• A decrease of 1 fps occurs when the weight of the arrow is 3 grains over the reference value. The reference value is 5 grains per pound draw weight.

• A decrease of 1fps occurs when the additional weight on the bowstring increases by 3 grains.

• As the speed through an arrow can never exceed the nominal speed, the lower limit of this adjustment is zero.

Combining these rules gives us this equation.

where v is the arrow speed in fps, IBO is the rated power, L is the draw length in inches, W is the additional weight on the bowstring in grains, A is the weight of the arrow in grains and D is the draw force in pounds. Assuming a bow has a rated power of 300fps, a draw length of 32inches, a draw force of 70pounds, uses an arrow with a weight of 400grains and has an additional weight of 5 grains on the bowstring.

Kinetic energy and momentum

Once the speed is known energy and momentum can be calculated from the weight of the arrow. Archers express kinetic energy in foot-pounds and momentum in slug-feet per second.

A is the weight of the arrow in grains, v is the velocity in fps. Kinetic energy depends on the square of the velocity so a higher velocity will dramatically increase kinetic energy. Momentum however increases with both the weight and velocity of the arrow. This is why archers often debate light and heavy arrows. Lighter arrows generally have an advantage in terms of kinetic energy while heavier arrows generally have an advantage in momentum and penetration.

A rough guideline for kinetic energy used in archery hunting:

Grain per pound and safe arrow weight.

The grain per pound (GPP) value is the weight of a finished arrow divided by the draw weight of the bow. It's a simple way to determine if an arrow is safe and what purpose it was designed for. Most bow manufacturers will give a GPP limit of 5; lighter arrows can damage the bow, similar to shooting without an arrow.

Tips for approaching actual values:

Measure the draw length and weigh your finished arrow. Estimations can affect both values by a few fps. The stated rating on the bow is a maximum value and not guaranteed so estimations should only be used as guidelines, and speed meter readings are always more reliable than calculations. To increase penetration without losing too much velocity you can add weight to the front of the arrowhead to move the center of gravity forward which can improve trajectory and penetration.

This calculation tool is for general planning and educational purposes only. The actual arrow speed will depend on the bow setup, string condition, and accessories used. So please verify your speeds with a chronograph before relying on these values for hunting purposes.