Circle Chord Calculator
Calculate chord length and related circle measurements
Chord length
How we calculated it
About the Circle Chord Calculator
Circle Chord Calculator finds the straight-line distance between two points on a circle from radius and central angle, or helps solve related chord geometry. Chords appear in fabrication, surveying and circular layout problems.
A chord is not the same as an arc. The chord cuts straight across the circle, while the arc follows the circumference between the same endpoints.
How to Use the Circle Chord Calculator
- Enter circle radius.
- Enter the central angle subtended by the chord, or another supported pair of measurements.
- Calculate chord length.
- Keep angle units correct and distinguish chord length from arc length.
How the Calculation Works
For radius r and central angle θ in radians, chord length c = 2r sin(θ/2).
If θ is supplied in degrees, it is converted before the sine calculation. The chord approaches the diameter when θ reaches 180°.
Worked example
Circle Chord Calculator Worked Example
Radius 10 cm and central angle 60°
Chord = 2×10×sin30° = 20×0.5 = 10 cm.
Result guide
Understanding Your Circle Chord Calculator Result
The chord is always less than or equal to the corresponding arc length for the same endpoints. At 180°, the chord is exactly the circle diameter. Chord geometry is also useful for checking sagitta, the maximum distance between a chord and its arc. When fabrication tolerances depend on that offset, chord length alone is not enough; pair the chord with radius or central angle so the full circular geometry is defined.
Before you rely on the answer
Assumptions and Limitations
- The points lie on the same circle.
- Radius is measured accurately.
- Angle unit is selected correctly.
Practical tip
Using This Result in Practice
For curved fabrication, verify whether drawings specify chord length, arc length or straight-line opening. These can differ enough to affect cuts and material layout.
Related calculations
Useful Calculations to Continue With
If you need the curved distance along the circumference instead, use the Arc Length Calculator.
If you need the area enclosed by the two radii and the arc, use the Circle Sector Calculator.
Common questions
Circle Chord Calculator FAQ
What is a chord?
A straight segment connecting two points on a circle.
What is the chord formula from angle?
c=2r sin(θ/2).
When is a chord equal to the diameter?
When the central angle is 180°.