How it works

This calculator helps you find the length of a chord in a circle. You can use either the circle's radius and the central angle subtended by the chord, or the radius and the sagitta (the height of the circular segment).

The Formula

Chord Length = 2 * r * sin(θ/2)
OR
Chord Length = 2 * sqrt(s * (2r - s)) Where:
r = Radius of the circle
θ = Central angle in radians
s = Sagitta (height of the circular segment)

Worked Example

1. Example: Finding Chord Length with Angle

   Imagine a circle with a radius of 10 cm. If a chord subtends a central angle of 60 degrees, what is its length? Using the formula: Angle in radians = 60 * (π/180) = π/3 radians Chord Length = 2 * 10 * sin((π/3)/2) Chord Length = 20 * sin(π/6) Chord Length = 20 * 0.5 = 10 cm Our calculator will show you this result instantly.

Tips, Assumptions & Limitations

• Ensure your central angle is in degrees or radians as specified. The calculator can handle both.
• The sagitta (s) must be positive and cannot be greater than the diameter (2r).
• A chord that passes through the center of the circle is its diameter, which is the longest possible chord.