Area of A Sector Calculator

Q: What is the difference between a sector and a segment?

A sector is the 'pie slice' shape bounded by two radii and an arc of a circle. A segment is the region between a chord and its corresponding arc. The segment area equals the sector area minus the triangle area formed by the two radii and the chord.

Calculate the area of a sector of a circle with interactive SVG diagram, step-by-step calculation, arc length, and comprehensive sector formulas using radius and central angle.

Free to useNo sign-up requiredUpdated Jan 2026

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Sector Area Calculator

Calculate area, arc length, and more with visual diagram

Quick Examples: Quarter Circle 60° Sector Semicircle π/2 radians

Radius (r)

Central Angle (θ)

Angle Unit

Decimal Precision

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About Area of A Sector Calculator

Welcome to the Area of a Sector Calculator, a comprehensive geometry tool that calculates the area of a circular sector with interactive diagrams, step-by-step formula breakdowns, and additional measurements like arc length, perimeter, and chord length. Whether you are a student learning circle geometry, a teacher preparing lessons, or a professional working with circular measurements, this calculator provides precise results with visual understanding.

What is a Sector of a Circle?

A sector is a portion of a circle enclosed by two radii and the arc between them. It looks like a "pie slice" or "pizza slice." The sector is defined by:

Radius (r): The distance from the center of the circle to any point on its circumference
Central Angle (θ): The angle formed at the center of the circle by the two radii
Arc: The curved portion of the circumference that bounds the sector

Area of a Sector Formula

The area of a sector can be calculated using two equivalent formulas, depending on whether the angle is measured in degrees or radians:

Formula with Degrees

Sector Area (Degrees)

$$A = \frac{\theta}{360°} \times \pi r^2$$

Formula with Radians

Sector Area (Radians)

$$A = \frac{1}{2} r^2 \theta$$

Where:

A = Area of the sector (in square units)
r = Radius of the circle
θ = Central angle (in degrees or radians)
π ≈ 3.14159265...

How to Use This Calculator

Enter the radius: Input the radius of your circle in any unit (cm, m, inches, etc.).
Enter the central angle: Input the central angle of the sector.
Select angle unit: Choose whether your angle is in degrees (0° to 360°) or radians (0 to 2π).
Set precision: Choose the number of decimal places for your results.
Calculate: Click the button to see the sector area along with an interactive diagram and additional measurements.

Additional Calculations

This calculator provides more than just the sector area. You will also see:

Arc Length

Arc Length Formula

$$s = r\theta \text{ (radians)} \quad \text{or} \quad s = \frac{\theta}{360°} \times 2\pi r$$

The arc length is the distance along the curved edge of the sector.

Perimeter of Sector

Sector Perimeter

$$P = 2r + s$$

The perimeter is the total boundary length: two radii plus the arc length.

Chord Length

Chord Length Formula

$$c = 2r \sin\left(\frac{\theta}{2}\right)$$

The chord is the straight line connecting the two endpoints of the arc.

Sector vs Segment

It is important to distinguish between a sector and a segment:

Property	Sector	Segment
Shape	Pie slice (bounded by 2 radii + arc)	Region between chord and arc
Boundaries	Two radii and one arc	One chord and one arc
Area Formula	A = ½r²θ	A = ½r²(θ - sin θ)
Contains center?	Yes (one vertex at center)	No

Converting Between Degrees and Radians

Understanding the relationship between degrees and radians is essential:

Full circle: 360° = 2π radians
Half circle: 180° = π radians
Quarter circle: 90° = π/2 radians

Conversion formulas:

Degrees to radians: multiply by π/180
Radians to degrees: multiply by 180/π

Real-World Applications

Understanding sector area has many practical applications:

Engineering: Calculating material for curved panels, fan blades, and turbine components
Architecture: Designing arched windows, domed ceilings, and curved walls
Food industry: Portioning pizzas, pies, and cakes evenly
Agriculture: Calculating coverage area for center-pivot irrigation systems
Graphics design: Creating pie charts and circular progress indicators
Navigation: Understanding radar sweep areas and field of view

Frequently Asked Questions

What is the formula for the area of a sector?

The area of a sector can be calculated using two equivalent formulas: A = (1/2)r²θ when the angle θ is in radians, or A = (θ/360°) × πr² when the angle θ is in degrees. Here, r is the radius of the circle and θ is the central angle of the sector.

How do I convert between degrees and radians?

To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. For example, 90° = 90 × π/180 = π/2 radians, and π radians = π × 180/π = 180°.

What is the difference between a sector and a segment?

A sector is the "pie slice" shape bounded by two radii and an arc of a circle. A segment is the region between a chord and its corresponding arc. The segment area equals the sector area minus the triangle area formed by the two radii and the chord.

How do I find the arc length of a sector?

Arc length is calculated using the formula s = rθ, where r is the radius and θ is the central angle in radians. If the angle is in degrees, use s = (θ/360°) × 2πr. The arc length is the curved distance along the circumference of the sector.

What is the perimeter of a sector?

The perimeter of a sector is the total boundary length, calculated as P = 2r + s, where r is the radius and s is the arc length. This includes two radii (straight edges) plus the arc (curved edge).

Related Tools

Arc Length Calculator - Calculate the arc length of a sector
Area of a Circle Calculator - Calculate the full circle area
Circumference Calculator - Calculate circle circumference

Reference this content, page, or tool as:

"Area of A Sector Calculator" at https://MiniWebtool.com/area-of-a-sector-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 28, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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