Segment Area Calculator

Segment Area Calculator

Find the area of a circular segment from a radius and a central angle.

Last updated: June 2026 | By Patchworkr Team

Circular Segment
Segment Area

Enter the radius and angle as real numbers.

What is the Formula?

A circular segment is the region between a chord and its corresponding arc.

A = 1/2 * r^2 * (theta - sin(theta))

That formula uses theta in radians, so degrees are converted before calculation.

How to Use

1. Enter the radius and the central angle.

2. Pick degrees or radians for the angle input.

3. Read the live area result in the right-hand panel.

Worked Example

For r = 6 and theta = 90 degrees:

theta = pi/2

A = 1/2 * 36 * (pi/2 - 1) ≈ 10.29

FAQ

Must theta be in radians?

The formula itself uses radians, so degrees are converted automatically.

Can the segment area be negative?

No. The tool rejects invalid angles and uses the correct segment formula.

What angle range is allowed?

Angles must be strictly between 0 and 2π radians after conversion.

Is this the minor segment?

Yes, the formula is valid for the provided central angle segment.

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