Sector Area Calculator

How to calculate the area of a sector of a circle?

The area of a sector of a circle is the portion of the circle's total area enclosed by two radii and the arc between them. It's like a "slice" or "pie piece" of the circle.

Formulas

The sector area is proportional to the central angle compared to the full 360° of the circle.

When the central angle is in degrees (most common in basic math/problems):

A = (θ / 360) × π r²

Where:

• A = sector area
• θ = central angle in degrees
• r = radius of the circle
• π ≈ 3.14159 (or use 3.14 for quick estimates)

Simplified alternative:

A = (θ × π r²) / 360

When the central angle is in radians (common in advanced math, physics, calculus):

A = (1/2) r² θ

Where θ is in radians.

(To convert degrees to radians: θ radians = θ degrees × π / 180)

Examples Calculations for Area of a Sector

Example 1 – Basic sector (degrees)

Radius r = 10 cm

Central angle θ = 72°

A = (72 / 360) × π × 10²

A = (0.2) × π × 100

A = 20π

A ≈ 62.83 cm²

Example 2 – Real-world pizza slice

Radius r = 7 inches (from center to crust)

Central angle θ = 60°

(a typical 6-slice pizza piece)

A = (60 / 360) × π × 7²

A = (1/6) × π × 49

A = 49π / 6

A ≈ 25.66 in²

Example 3 – Using radians

Radius r = 5 m

Central angle θ = π/3 radians

(60° = π/3 rad)

A = (1/2) × r² × θ

A = (1/2) × 25 × (π/3)

A = (25π) / 6

A ≈ 13.09 m²