Chord Length Calculator

A chord is a straight line connecting two points on a circle. This finds its length.

How the Math Works

The Chord Length Calculator uses the fundamental trigonometric relationship between a circle's radius and its central angle to determine chord length. When you input the radius (r) and central angle (θ) in degrees, the formula chord = 2r·sin(θ ÷ 2) first converts the angle to radians and then applies the sine function to half that angle. This works because a chord creates an isosceles triangle with two radii, and the sine function relates the half-chord to the radius through the angle at the circle's center. The multiplication by 2 accounts for both halves of the chord, giving you the complete straight-line distance between two points on the circle's circumference.

Practical Applications

To use this calculator effectively, first identify the circle's radius and measure or determine the central angle that subtends the chord you want to find. For practical applications like construction or engineering, you might measure the radius directly or calculate it from the circle's diameter. The central angle can be measured using a protractor for simple geometric problems or calculated from arc length measurements. This calculation is essential when working with circular structures, such as determining the length of a circular beam, pipe section, or architectural element where direct measurement is difficult or impossible.

Day-to-Day Use

Understanding chord length helps in everyday situations involving circular objects or spaces. When setting up a circular garden or patio, you can estimate material needs by calculating chord lengths for different sections. Sports coaches use this concept to design circular training drills or to calculate distances players must run around stadium tracks. Even when arranging furniture in round rooms or hanging decorations at specific intervals around a circular ceiling, knowing chord lengths helps determine spacing and fit. The calculator simplifies these measurements without requiring complex trigonometric calculations or specialized tools.

Worked example

Radius 5, angle 60° → 2·5·sin(30°) = 5.

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