How to Calculate the Chord of a Circle

By Michael Keenan; Updated April 24, 2017

A chord is a straight line that connects two points on the circumference of the circle without passing through the center. If the line passes through the center of the circle, it is a diameter. To calculate the chord length, you need to know the radius and either the central angle or the perpendicular distance to the center. The central angle of a chord is the angle formed by drawing lines from the points that the chord touches the circle to the center of the circle. For example, if a chord went from point A to point B on the circle and the center of the circle was point O, the central angle would be formed by the lines AO and BO. The perpendicular distance to the center is the length of the line perpendicular to the chord that goes through the center of the circle.

Radius and Central Angle

Divide the central angle by 2. For example, if the central angle equals 50, you would divide 50 by 2 to get 25.

Use your calculator to calculate the sine of half the central angle. In this example, the sine of 25 equals about 0.4226.

Multiply the result from Step 2 by the radius. Continuing the example, assuming the radius is 7, you would multiply 0.4226 by 7 and get about 2.9583.

Double the result from Step 3 to calculate the length of the chord. Finishing this example, you would multiply 2.9583 by 2 to find the chord's length equals about 5.9166.

Radius and Distance to Center

Square the radius. In this example, the radius will be 10 so you would get 100.

Square the perpendicular distance to the center. In this example, the distance to the center will be 6, so you would get 36.

Subtract the results from Step 2 from the radius squared. Continuing the example, you would subtract 36 from 100 to get 64.

Take the square root of the result of Step 3. In this example, the square root of 64 equals 8.

Multiply the result from Step 4 by 2 to find the chord length. Finishing the example, you would multiply 8 by 2 to find the chord length equals 16.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."