What is the difference between a chord and an arc?

A chord is the straight line segment connecting two points on a circle. An arc is the curved portion of the circle between those same two points. The chord is always shorter than or equal to the arc.

What happens to the chord length when the central angle is 180 degrees?

At 180 degrees the chord spans the full diameter of the circle, so chord = 2r x sin(90) = 2r. It is the longest possible chord.

Can I use this formula if I only know the arc length, not the angle?

No — you need either the central angle or the radius plus some other measurement. You can derive the central angle from arc length using angle = arc length / r (in radians), then apply the chord formula.

Chord Length Calculator

Calculate the straight-line chord length of a circle from the radius and the central angle in degrees. Uses the formula chord = 2r sin(theta/2). Handy for circular geometry problems.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

Embed this tool on your site

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How to use this tool

Enter radius and central angle in the fields above.
Results update instantly as you type — or click Calculate.
Read your chord length and the full breakdown beneath it.

Formula

chord = 2r * sin(theta/2), theta in degrees

How it works

Divide the central angle by 2, convert to radians, then: chord = 2r sin(θ/2).

Worked example

60-degree chord in unit circle

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.

Common mistakes to avoid

Entering the full central angle instead of half the angle — the formula uses sin(theta/2), so a 90 degree arc requires sin(45), not sin(90).
Mixing degrees and radians: if you compute sin in radians but enter the angle in degrees, the result will be wildly wrong.
Confusing the chord with the arc length — the chord is the straight line between two endpoints, not the curved arc along the circle.

Key terms

Frequently asked questions

What is the difference between a chord and an arc?: A chord is the straight line segment connecting two points on a circle. An arc is the curved portion of the circle between those same two points. The chord is always shorter than or equal to the arc.
What happens to the chord length when the central angle is 180 degrees?: At 180 degrees the chord spans the full diameter of the circle, so chord = 2r x sin(90) = 2r. It is the longest possible chord.
Can I use this formula if I only know the arc length, not the angle?: No — you need either the central angle or the radius plus some other measurement. You can derive the central angle from arc length using angle = arc length / r (in radians), then apply the chord formula.