Chord Length Calculator

Calculate chord lengths, radii, and central angles in circles

Enter the known values to calculate the chord length, radius, or central angle of a circle. A chord is a straight line connecting two points on a circle.

Formula

c = 2r × sin(θ/2)

Where: c = chord length, r = radius, θ = central angle in radians

Examples

  • Circle with radius 5, central angle 60°: Chord length = 5 units
  • Circle with radius 10, chord length 12: Central angle ≈ 73.74°
  • Chord length 8, central angle 90°: Radius ≈ 5.66 units
Other Titles
Understanding Chord Length Calculator: A Comprehensive Guide
Explore the mathematical concept of chord lengths, their relationship with radii and central angles, and applications in geometry and engineering

Understanding Chord Length Calculator: A Comprehensive Guide

  • Chords are fundamental elements in circle geometry
  • They connect any two points on a circle's circumference
  • Chord calculations have widespread applications in engineering and design
A chord is a straight line segment that connects any two points on a circle's circumference. It's one of the most basic yet important elements in circle geometry.
The length of a chord depends on both the radius of the circle and the central angle it subtends. This relationship forms the basis for many geometric calculations.
Understanding chord lengths is essential for solving problems in architecture, engineering, navigation, and various fields that deal with circular structures.

Basic Examples

  • The diameter is the longest possible chord in any circle
  • Two chords of equal length in the same circle subtend equal central angles
  • Perpendicular chords create right angles at their intersection point
  • Chord calculations are used in bridge arch design
  • Musical instrument design uses chord geometry for sound holes