The Math in Archery

Mathematical Archery

Christina Sng for Maths@Singapore

Between you and me, I’ve always wanted to be an archer like Katniss and Legolas. Archers were always cool and composed, and they made their shot.

I tried archery once. The bow was heavy, the arrow hard to balance, and I shot my arrows everywhere but the bulleye.

Like pool, there is a lot of math in archery. While you don’t need to utilize it to enjoy the sport, the understanding gives you a greater sense and control.

Here are some math in archery calculations you can make:

1.  Measuring Draw Length

The draw length is the distance you pull back the string for a comfortable and proper shooting form. 

To measure your draw length, have the archer stand with arms up in a T shape. 

A friend measures from the tip of one middle finger, across the back, to the tip of the other middle finger. 

Take that number and divide it by 2.5. That is your draw length.

2.  Calculate Arrow Weight

Measure the distance from the base of the arrow’s nock groove to the shaft’s end.

Multiply it by the grains per inch (GPI) written on the side of the arrow.

The resulting number is approximately the arrow’s weight in grains.

3.  The Front-of-Centre Formula

This formula tells you how weight is distributed throughout the arrow in terms of the percentage of an arrow’s total weight in its front half. 

This helps increase your accuracy, especially with long range shooting.

Divide the arrow’s length by 2.

Find the balance point, where the arrow balances perfectly. Mark the point, and measure from there to the nock’s throat.

Subtract the centre of the arrow measurement from the balance point.

Multiply the answer by 100.

Divide the answer by the arrow’s overall length. This will give you the arrow’s Front-of-Centre percentage.

For a more detailed explanation with videos, visit

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Thanks to Alireza Sahebi @alirzasahb for making this photo available freely on Unsplash 🎁