How does the Chord Length Calculator work?

Chord = 2r × sin(θ/2) Then: Sagitta = r × (1 − cos(θ/2)) Then: θ is the central angle in radians Then: Maximum chord is the diameter (θ = 180°).

Can you give an example of how to use the Chord Length Calculator?

Example: Input r = 10, θ = 60° gives a result of Chord = 2×10×sin(30°) = 10.

Is the Chord Length Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Chord Length Calculator?

Our Chord Length Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Chord Length Calculator

Radius

Central Angle

A chord is a straight line segment connecting two points on a circle. The chord length calculator uses the radius and central angle to find both the chord length and the sagitta (the height of the arc above the chord).

Symbol	Name	Unit	Description
r	radius	length	—
θ	central angle	radians	—
c	chord length	length	—
s	sagitta (arc height)	length	—

Angle (°)	Chord	Sagitta
30	5.18	0.67
60	10.00	1.34
90	14.14	2.93
120	17.32	5.00
180	20.00	10.00

References

›Chord (geometry) — Wolfram MathWorld

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Chord Length Calculator

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Chord Length for r = 10

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Chord Length Calculator