Arc Length Calculator

Arc length and chord, with the radian conversion shown.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Radius

Central angle

Arc length (units)

10.472

1.0472 radians · chord 10 units

Arc length10.472 units

Chord length10 units

Arc minus chord0.472 units

Angle in radians1.0472

Full circumference62.8319 units

Sector area52.3599 units²

Arc length is simply rθ once the angle is in radians, which is the entire reason radians exist as a unit — they are defined so that this formula has no conversion factor in it. The arc always exceeds the chord, and the gap widens with the angle: 0.472 units here.

How the Arc Length Calculator works

Arc length is simply rθ once the angle is in radians, which is the whole reason radians exist as a unit — they are defined so this formula carries no conversion factor. Degrees need dividing by 180 and multiplying by π first, and this page shows that step.

Also known as: arc length formula · length of an arc calculator · chord length calculator · arc of a circle

Where to go next

The Arc Length question rarely arrives on its own. These are the ones that usually come with it:

Circle Sector Calculator — Sector area, arc length and chord from a radius and an angle.
Circle Calculator — Area, circumference, radius and diameter from any one of them.
Pythagorean Theorem Calculator — The missing side of a right triangle, plus its angles and area.
Percentage Calculator — Every common percentage question in one place.

Sources

NIST Digital Library of Mathematical Functions

Frequently asked questions

How do I calculate arc length?

Multiply the radius by the angle in radians. For degrees, convert first: a 60° arc on a radius of 10 is 10 × (60π⁄180) = 10.47 units.

Why do radians make the formula simpler?

Because a radian is defined as the angle whose arc equals the radius. That definition makes arc length exactly rθ, with no constant to remember.

How long is the chord?

2r sin(θ⁄2). It is always shorter than the arc, since a straight line is the shortest path between two points.

What fraction of the circle is my arc?

The angle divided by 360. A 60° arc is one sixth of the circumference.

Put this calculator on your own site

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The one-line version

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