What is a circular segment?

A circular segment is the region of a disk enclosed by a chord and the arc that the chord subtends. It is not the same as a sector, which is the "pie slice" region bounded by two radii and an arc.

What is the formula for the perimeter of a segment?

Perimeter = arc length + chord length = rθ + 2r·sin(θ/2), where r is the radius and θ is the central angle in radians.

Does a segment perimeter include the chord?

Yes. The boundary of a circular segment consists of the arc and the chord, so the perimeter is the sum of both. If you need only the arc length, the result is also shown separately.

What is the difference between a minor and major segment?

A minor segment corresponds to a central angle less than 180 degrees (π radians). A major segment corresponds to an angle greater than 180 degrees. This calculator handles both cases.

Can I enter the angle in radians?

Yes. Toggle the angle unit switch to Radians and enter the angle directly. The calculator applies the formula without any conversion.

Perimeter of a Segment Calculator

Name: Perimeter of a Segment Calculator
Availability: InStock
Author: Nham Vu

Calculate the perimeter of a circular segment — arc length plus chord length — from radius and central angle.

Segment Inputs

Radius (r)

units

Central Angle (θ)

Segment diagram (not to scale)

Enter radius and angle, then click Calculate.

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Summary

Calculate the perimeter of a circular segment — arc length plus chord length — from radius and central angle.

How it works

Enter the radius of the circle.
Enter the central angle in degrees or radians.
The calculator converts degrees to radians if needed.
Arc length is computed as r × θ (radius times angle in radians).
Chord length is computed as 2r × sin(θ / 2).
The perimeter is arc length + chord length.

Use cases

Engineering designs involving curved cuts or arched panels.
Architecture — calculating material needed for arched window frames.
Woodworking and metalworking templates with circular cutouts.
Geometry homework and exam preparation.
Surveying land parcels bounded by arc sections.
Manufacturing gaskets or seals with circular segment shapes.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu