Sector Area Formula
Calculate the area of a pie-shaped region of a circle.
Used in data visualization, construction, and geometry.
The Formula
A = ½r²θ (radians) or A = (θ/360) × πr² (degrees)
A sector is a "pie slice" of a circle. Its area is a fraction of the total circle area, proportional to the central angle.
Variables
| Symbol | Meaning |
|---|---|
| A | Area of the sector |
| r | Radius of the circle |
| θ | Central angle (in radians or degrees) |
Example 1
Find the area of a 90° sector with radius 6 cm
A = (90/360) × π × 6²
A = 0.25 × π × 36
A ≈ 28.27 cm²
Example 2
A sprinkler covers a sector of π/3 radians with reach of 10 m
A = ½ × 10² × (π/3)
A = ½ × 100 × 1.047
A ≈ 52.36 m²
When to Use It
Use the sector area formula when:
- Calculating the area covered by a sprinkler or radar sweep
- Designing pie charts and proportional diagrams
- Finding land area for curved property boundaries
- Computing material needed for fan-shaped or wedge-shaped pieces