What is a chord in a circle?

A chord is a straight line segment connecting two points on a circle's circumference (not necessarily passing through the center).

How is chord length calculated?

Chord length = 2 x radius x sin(angle/2), where the angle is the central angle subtended by the chord, in the same units the sine function expects.

What's the longest possible chord in a circle?

The diameter — a chord that passes through the center is the longest chord possible, equal to twice the radius.

Chord Length Calculator - CalculatorLabs.net

Chord Length Calculator

A chord is any straight line connecting two points on a circle.

Circle Radius (r)

Distance from Center to Chord (d)

Instant Result

Chord Length -

Central Angle -

What Is a Chord Length Calculator?

A chord is any straight line connecting two points on a circle. If you know the circle's radius and how far the chord sits from the center (measured perpendicularly), you can find the chord's exact length and the central angle it spans. This is handy for arches, bridge trusses, and any curved design work.

How to Use This Chord Length Calculator

Measure the circle's radius r and the perpendicular distance d from the center to the chord.
Enter both values into the fields above.
Click Calculate to get the chord length and the central angle it subtends.

Formula

Chord Length = 2 × √(r² − d²)
Central Angle = 2 × arccos(d / r)

Worked Example

A circular arch has a radius of 5 m, and the chord (the straight span at the bottom) sits 3 m from the center. Chord Length = 2 × √(5² − 3²) = 2 × 4 = 8 m. Central Angle = 2 × arccos(3/5) ≈ 106.26°.