Chord Length Calculator
Calculate the length of a chord from the circle radius and central angle.
About Chord Length Calculator
The chord length of a circle is found using the formula 2r·sin(θ/2), where r is the radius and θ is the central angle in radians.
Formula
Chord Length
chord = 2r × sin(θ/2)
- r
- Radius of the circle
- θ
- Central angle subtended by the chord
Worked example
With the default values below, Chord Length Calculator returns Chord Length of 10.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Radiusminimum 0 units
- 10 units
- Central Angleaccepts 0–360 °
- 60 °
Results
- Chord Length
- 10.0000 units
Step by step
- 1Apply chord formula= 10.0000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the longest possible chord?
The diameter — which corresponds to a central angle of 180°.
Does this work for angles over 180°?
Yes — for reflex angles the formula still gives the chord length, which is the same as for the supplementary angle.