Chord Length Calculator

About this calculator

The chord length formula, c = 2r × sin(θ/2), gives the straight-line distance between two points on a circle's circumference given the circle's radius r and the central angle θ that the chord subtends at the center — a direct consequence of splitting the isosceles triangle formed by the two radii and the chord into two right triangles.

Chord length calculations appear throughout engineering and design: civil engineers use them to lay out circular road curves and railway track curvature, mechanical engineers use them for gear tooth spacing and pulley design, and the same formula underlies CNC and CAD software when converting arc geometry into straight-line segments for machining or rendering.

This calculator takes a circle's radius and the central angle in degrees and returns the exact length of the chord that connects the two endpoints of that arc.