How to Calculate Circular Error of Probability

By Kim Sarah
Shooting practice often uses a target

The circular error of probability refers to the average distance between a target and the terminal end of an object's path of travel. This is a common calculation problem in the shooting sports, where a projectile is launched towards a particular destination. In most cases, the shot will not hit the target when fired multiple times. This anticipated room for error considers the distance of each missed shot from the intended target. Simple calculations can determine the average error for all of the shots. The root mean square is primarily used for this process.



Shoot ammunition from the shooting device towards a target. The more shots you fire, the more accurate the calculation will be.

Measure the distance that each shot is off target with a ruler. Record these numbers with a pencil and paper.

Square each number in the list individually. Multiply each number by itself.

Find the average of all the squared numbers by adding all the numbers together and dividing them by how many numbers are listed.

Find the square route of the average of all the numbers to determine the circular error of probability.

About the Author

Kim Sarah has been a writer since 2000. Her work has appeared on NECN, WCTR-TV3 and in the "Torch" university newspaper, among other publications. Sarah received a Bachelor of Arts in communications from Worcester State University and a Master of Arts in journalism from Roosevelt University. She is also studying nursing and computer science at Indiana State University.