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Arc Length Calculator

Find the arc length, sector area, chord length and segment area of a circle from the radius and angle.
By MD Sayem Updated

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Arc length calculator in short
  • Finds the arc length from the radius and central angle.
  • Also gives the sector area, chord length, segment area and sector perimeter.
  • Works in degrees or radians.
  • Can find the angle from the radius and arc length.
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How to use the arc length calculator

1

Choose what you know

Radius and angle, or radius and arc length.

2

Enter the radius

For example 10.

3

Enter the angle or arc length

For example 60°, or switch to radians.

4

Read the results

Arc length, sector area, chord and more.

Arc length and sector formulas

An arc is part of a circle’s edge. Its length depends on the radius and the central angle. With the angle in radians, the arc length is simply the radius times the angle.

Formulas (θ in radians)

Arc length s = rθ

Sector area = ½r²θ

Chord = 2r sin(θ ÷ 2)

Segment area = ½r²(θ − sin θ)

To convert degrees to radians, multiply by π ÷ 180.

Example 1: radius 10, angle 60°

60° = 1.047198 rad.

  • Arc length 10.471976
  • Sector area 52.359878
  • Chord length 10
  • Segment area 9.058607

Example 2: one radian

Radius 10, arc length 10.

  • Angle 1 rad = 57.29578°
  • Sector area 50

Where arc length is used

Geometry and trig

Solve arc and sector questions in degrees or radians.

Engineering

Find the length of curved parts and bends.

Landscaping

Measure curved paths and garden edges.

Design

Size pie charts, arches and curved cuts.

Related tools

Find a full circle’s area and circumference with the circle calculator, or work with angles in the trig calculator.

Arc length calculator FAQ

s = rθ with θ in radians, or s = 2πr × (angle ÷ 360) with the angle in degrees.

About 10.47.

The pie-slice shaped part of a circle between two radii and the arc.

A chord is the straight line between the arc’s ends; the arc is the curved part.

Divide the arc length by the radius to get the angle in radians.

The area between a chord and its arc.

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Works with WordPress, Wix, Squarespace, Webflow and most site builders that allow HTML. How embedding works.

Estimates, not advice

PureCalculate’s calculators give estimates for planning and education. They aren’t financial, tax or legal advice. Fees and tax rules change, so check the official source before making a decision. Spotted a mistake? Please tell us through the contact page.

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