Geometry

Area of a Sector

Formula

A = (θ/360) × π × r²

What is Area of a Sector?

A sector is a pie-shaped portion of a circle. Its area is a fraction of the circle's total area, determined by the central angle θ as a fraction of 360 degrees.

Variables

A
A — Area of the sector
θ
θ — Central angle in degrees
r
r — Radius
π
π — Pi (approximately 3.14159)

Worked Examples

Example 1

Find the area of a sector with radius 8 cm and angle 90°.

Solution:

A = (90/360) × π × 64 = (1/4) × 64π = 16π ≈ 50.27 cm²

Frequently Asked Questions

Related Formulas

Area of a Circle

A = π × r²

Circumference of a Circle

C = 2 × π × r

Area of a Rectangle

A = l × w

Area of a Triangle

A = ½ × b × h

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