How to Find the Radius of an Arc

By Michael O. Smathers
arc image by Snezana Skundric from

In high school geometry, you will study arcs, or segments of a circle. No matter what the size of the arc is, you can use it to determine the radius and size of the circle to which the arc belongs. This skill is useful for construction and engineering applications. Using the measurements derived from the arc's chord and the line bisecting it, you can determine the radius of an arc.

Draw the arc on a sheet of paper.

Connect the two points of the arc with a ruler and draw a line between them.

Set the compass point on one end of the chord and move the pencil side to at least halfway down the length of the chord. Draw an arc.

Draw an arc passing through the chord. Repeat for the opposite side of the chord.

Connect the intersection points of the two arcs you just drew with a line. This line should run perpendicular to the chord and pass exactly through its midpoint.

Measure the length of the chord and the length of the bisecting line segment from the chord to the top of the arc.

Enter the values into the formula (h/2) + (w^2/8h), where h is the arc height and w is the length of the chord. The result will be the radius.

About the Author

Michael Smathers studies history at the University of West Georgia. He has written freelance online for three years, and has been a Demand Studios writer since April 2009. Michael has written content on health, fitness, the physical sciences and martial arts. He has also written product reviews and help articles for video games on BrightHub, and martial arts-related articles on Associated Content.