What is a circular segment?

A circular segment is the region enclosed between a chord (a straight line connecting two points on a circle) and the arc between those two points. It is different from a sector, which uses two radii instead of a chord.

What formula does this calculator use?

The area of a circular segment is A = (r² / 2)(θ − sin θ), where r is the radius and θ is the central angle in radians. For degree input the calculator converts first: θ_rad = θ_deg × π / 180.

What is the difference between a segment and a sector?

A sector is a "pie slice" bounded by two radii and an arc. A segment is the region between a chord and an arc — essentially the sector minus the triangle formed by the two radii and the chord.

Does the angle have to be less than 360 degrees?

Yes. The central angle must be between 0° and 360° (exclusive). An angle of exactly 360° would describe the full circle, not a segment.

Can I enter the angle in radians?

Yes. Use the Degrees / Radians toggle to switch input mode. The valid range in radians is 0 to 2π (approximately 6.2832).

What units does the area use?

The area unit is the square of whatever unit you use for the radius. If the radius is in centimeters, the area is in cm². The calculator labels the result accordingly.

Area of Circular Segment Calculator

Name: Area of Circular Segment Calculator
Availability: InStock
Author: Nham Vu

Enter a circle radius and central angle to instantly calculate the area of the circular segment.

Inputs

Radius (r)

Central Angle (θ)

Enter value between 0 and 360 degrees.

Segment Area

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Enter values and press Calculate

Diagram

Summary

Enter a circle radius and central angle to instantly calculate the area of the circular segment.

How it works

Enter the circle radius in any unit (cm, m, in, etc.).
Enter the central angle either in degrees or radians using the toggle.
The calculator converts degrees to radians when needed.
It applies the formula A = (r² / 2)(θ − sin θ) to get the segment area.
Results update instantly as you type, with the formula steps shown below.

Use cases

Engineering and architecture — sizing curved cut-outs or panels.
Surveying — computing land area bounded by a circular arc and chord.
Woodworking — calculating the waste area when cutting circular arcs.
Physics — finding cross-sectional areas of partially filled cylindrical pipes.
Mathematics education — verifying homework on circle geometry.
CAD/CAM — pre-computing material needed for circular segments.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu