# Arrow Speed Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: May 13, 2022

This arrow speed calculator allows you to accurately determine the speed of an arrow. While it is based on the bow speed IBO specification, you can input the individual settings of your bow. It will give you a rough idea of how fast an arrow travels after changing the bow from the recommended specifications. You can use the results obtained from this archery calculator in the projectile motion calculator to analyze the arrow's path.

## Understanding bow speed IBO specification

Most professional bows use the IBO (International Bowhunting Organization) specification. This specification determines the arrow speed, provided that you keep the following parameters:

• Draw length equal to 30 inches;
• Draw weight equal to 70 pounds; and
• arrow weighing 350 grains.

If you deviate from these parameters, the arrow speed will not equal the one given by the specification. Nevertheless, most archers do not use these exact parameters. This is where this bow speed calculator comes in handy; it allows you to examine how the arrow will behave under a different bow setting.

## Archery calculator principles

You should adjust the arrow speed given by the IBO specification according to the following rules:

• For every inch of draw length under 30″, subtract 10 ft/s from the IBO value.
• For every inch of draw length above 30″, add 10 ft/s to the IBO value.
• For every 3 grains of total arrow weight above draw weight multiplied by 5, subtract 1 ft/s from the IBO value.
• For every 3 grains of additional weight on the bowstring, subtract 1 ft/s from the IBO value.

All of these rules can be put in one common equation:

\footnotesize \begin{align*} v =\ &\text{IBO} + (L - 30) \times 10 - W\!/3\ +\\ &\min(0, -(A - 5D\!/3) \end{align*}

where:

• $v$ – Actual arrow speed in ft/s;
• $\text{IBO}$ – Arrow speed according to the IBO specification in ft/s;
• $L$ – Draw length in inches;
• $W$ – Additional weight on the bowstring in grains;
• $A$ – Arrow weight in grains; and
• $D$ – Draw weight in pounds.

You can also use the arrow speed calculator to find the momentum and the kinetic energy of the arrow. These are calculated as follows:

\footnotesize \begin{align*} \text{momentum} &= A \cdot v\\\\ \text{kinetic energy} &= \frac{A \cdot v^2}{2} \end{align*}

Our arrow speed calculator converts the units automatically. If you try to do all of these calculations by hand, keep in mind what units you actually use!

## How fast does an arrow travel?

Let's consider the following example: you are analyzing the bow of IBO 300. You want to know the arrow's speed when you increase both the draw length and the arrow weight.

1. Choose the draw length. Let's say it is equal to 32".
2. Decide on the draw weight and the arrow weight. Let's say you keep the regular peak draw weight of 70 lbs but use arrows weighing 400 grains.
3. If there is any additional weight on the bowstring, write it down. Let's assume this weight is equal to 5 grains.
4. Input all of these values into the formula for arrow speed:
\footnotesize \quad \begin{align*} v &=\ \text{IBO} + (L - 30) \times 10 - W\!/3\ +\\ &\qquad\min(0, -(A - 5D/3)\\\\ &=\ 300 + (32 - 30) \times 10 - 5/3\ +\\ &\qquad\min(0, -(400 - 5\times70)/3)\\\\ &=\ 300 + 2 \times 10 - 1.66\ +\\ &\qquad\min(0, -(400 - 350)/3)\\\\ &=\ 300 + 20 - 1.66\ +\\ &\qquad\min(0, -50/3)\\\\ &=\ 318.33 - 16.67\\\\ &=\ 301.67\ \text{ft/s} \end{align*}
Bogna Szyk
Bow IBO rating
ft/s
Draw length of the bow
in
Peak draw weight
lb
Arrow weight
gr
Additional weight on string
gr
Arrow speed
ft/s
Momentum
Ns
Kinetic energy
ft-lbs
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