How to Calculate Chord Length

By David Sarokin; Updated April 24, 2017
You can calculate chord length from two known variables.

A chord is a line segment connecting any two points on the circumference of a circle. The circle's diameter—the line segment through the center—is also its longest chord. You can calculate the length of a chord from the length of the radius and the angle made by lines connecting the circle's center to the two ends of the chord. You can also calculate chord length if you know both the radius and the length of the right bisector, which is the distance from the center of the circle to the center of the chord.

When the Radius and Central Angle Are Known

Multiply the radius by two, which is equal to the diameter of the circle.

Divide the central angle (the angle made by lines connecting the circle's center to the two ends of the chord) by two.

Find the sine of the divided angle using a calculator or sine table.

Multiply your values to calculate the chord length.

When the Radius and Distance to the Center Are Known

Multiply the radius by itself to find its square.

Multiply the distance to the center (right bisector) by itself to find its square.

Subtract the smaller value from the larger value.

Find the square root of the value you calculated from the subtraction.

Double the square root to determine the chord length.

Tip

In the examples that follow, r = radius, c = central angle, d = distance to center.

For a circle with r = 5 and c = 60 degrees: chord length = 2r sin (c/2) = 2_5 (sin 30) = 10_0.5 = 5

For a circle with r = 5 and d = 3: chord length = 2_(r^2 – d^2)^1/2 = 2(5_5 – 3_3)^1/2 = 2(25 – 9)^1/2 = 2_(16^1/2) = 2*4 = 8

About the Author

David Sarokin is a well-known specialist on Internet research. A former researcher with Google Answers, he has been profiled in the "New York Times," the "Washington Post" and in numerous online publications. Based in Washington D.C., he splits his time between several research services, writing content and his work as an environmental specialist with the federal government.