A sector is a "pie slice" of a circle bounded by two radii and the arc between them. The central angle determines how large the slice is.

What formula does this calculator use?

It uses A = (theta / 2) * r², where theta is the central angle in radians and r is the radius. If you enter degrees, the tool converts them to radians first using theta_rad = theta_deg * (pi / 180).

What is a full circle in degrees and radians?

A full circle is 360 degrees, which equals 2π radians (approximately 6.2832 radians).

Can the angle be larger than 360 degrees?

For a standard sector, the angle should be between 0 and 360 degrees (0 to 2π radians). Angles outside this range are not geometrically meaningful for a single sector and the tool will show a validation error.

What units is the area returned in?

The area is returned in the square of whatever unit you used for the radius. For example, if the radius is in centimeters, the area is in square centimeters (cm²).

Area of a Sector Calculator

Name: Area of a Sector Calculator
Availability: InStock
Author: Nham Vu

Enter the radius and central angle (degrees or radians) to instantly compute the area of a circular sector.

Sector Parameters

Radius (r)

Any positive unit (cm, m, in, …)

Angle Unit

Central Angle (θ in degrees)

Enter a value between 0 and 360.

Result

Enter values and click Calculate.

Summary

Enter the radius and central angle (degrees or radians) to instantly compute the area of a circular sector.

How it works

Enter the radius of the circle.
Choose whether your angle is in degrees or radians.
Enter the central angle value.
Click Calculate to see the sector area instantly.
Use the Reset button to clear all fields and start over.

Use cases

Compute the area of a pie-chart slice given an angle.
Solve geometry homework and exam problems involving circles.
Calculate the material needed for a fan-shaped piece.
Determine the area of a camera or sensor field of view.
Design curved architectural elements or garden beds.
Verify manual calculations for engineering drawings.

Frequently Asked Questions

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