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Arc Length Calculator: Arc, Sector, Chord and Segment

This free arc length calculator finds the length of an arc, the area of its sector, the length of its chord and the area of the circular segment from a radius and an angle.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

An arc is a piece of a circle’s edge. Curved paths, roads, arches and pizza slices need its length and the area it encloses.

Enter the radius and the central angle.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

With θ in radians: arc length = rθ, sector area = ½ r² θ, chord = 2r sin(θ ÷ 2) and segment area = ½ r² (θ − sin θ). Degrees are first converted to radians by multiplying by π ÷ 180.

Worked Example

With radius 10 and an angle of 90°, the arc length is 15.708, the sector area 78.54, the chord 14.142 and the segment area 28.54.

Common Uses

  • Curved paths and roads.
  • Arches and windows.
  • Pizza and pie slices.
  • Gear and wheel design.

Tips and Common Mistakes

  • Check whether your angle is in degrees or radians.
  • The angle must be between 0 and 360 degrees.
  • The chord is always shorter than the arc.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the circle calculator, ellipse calculator, regular polygon calculator, sphere calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Arc length = r × θ, with θ in radians. In degrees, arc length = 2πr × (θ ÷ 360).
The slice of a circle between two radii and the arc, like a slice of pizza.
The straight line joining the two ends of the arc. Its length is 2r × sin(θ ÷ 2).
The part of the circle between the chord and the arc. Its area is the sector area minus the triangle.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.