How does the Sector and Arc Calculator work?

Area = (θ/360) × πr² for degrees Then: Area = ½r²θ for radians Then: Full circle = 360° = 2π radians Then: Half circle sector = semicircle.

Can you give an example of how to use the Sector and Arc Calculator?

Example: Input r = 8, θ = 45° gives a result of Area = (45/360)×π×64 ≈ 25.13.

Is the Sector and Arc Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Sector and Arc Calculator?

Our Sector and Arc Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Sector and Arc Calculator

Sector Area Calculator

Radius (r)

Angle

Calculates the area of a circular sector (pie-slice shaped region) given radius and angle. A sector is defined by two radii and the arc between them.

Symbol	Name	Unit	Description
r	radius	length	—
θ	central angle	degrees or radians	—
A	sector area	length²	—

r	θ (°)	Area
5	90	19.63
8	45	25.13
10	120	104.72
12	60	75.40

References

›Sector area — Math is Fun

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Sector and Arc Calculator

Sector Area Calculator

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Sector Area Calculator