Circle Chord Calculator
Calculate chord length and arc length from a circle’s radius and central angle.
How it works
- 1Enter the circle’s radius and the central angle in degrees.
- 2Chord length is computed as 2r·sin(θ/2) — the straight line joining the two endpoints of the arc.
- 3Arc length is computed as r·θ (θ converted to radians), the curved distance along the circle.
Use cases
- Engineering and construction: sizing curved beams, arches, or tunnel cross-sections.
- Geometry coursework: verifying chord and arc relationships in circle theorems.
- Navigation and mapping: measuring straight-line distances across circular survey plots.
Frequently asked questions
What is a chord?
A chord is the straight line segment joining two points on a circle’s circumference. Its length depends on the radius and the central angle subtended between those points.
How is chord length different from arc length?
Chord length is the direct straight-line distance (2r·sin(θ/2)), while arc length is the curved distance along the circle (r·θ). The arc is always longer than or equal to the chord.
What happens when the central angle is 180°?
At 180° the chord becomes a diameter (2r) and the arc becomes a semicircle (π·r) — the maximum values each can reach for a given radius.
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