Sector Area Calculator - Circle Sector
Calculate the area of a circle sector from radius and central angle in degrees or radians. Shows arc length, perimeter, and step-by-step formula.
Formula
A = πr²(θ/360°)
The area is the total area of the circle multiplied by the fraction of the circle covered by the angle.
Worked Examples
Example 1: Pizza Slice
Problem:12" pizza (r=6), 45° slice
Solution:Area = π(6²)(45/360) = 36π(0.125) = 4.5π
Result:14.14 sq in
Example 2: Pacman Shape
Problem:r=10, 300° angle
Solution:Area = π(100)(300/360) = 100π(0.833)
Result:261.80
Frequently Asked Questions
What is a Circle Sector?
A sector is a portion of a circle enclosed by two radii and an arc. Think of it as a "slice of pizza".
What is the formula for Sector Area?
Area = πr² × (θ/360) for degrees. For radians: Area = ½r²θ.
What is the difference between a Sector and a Segment?
A sector includes the center of the circle (the pointy part of the slice). A segment is the region between a chord and an arc (the crust part without the point).
Can area be calculated without angle?
Yes, if you know the arc length (L) and radius (r), Area = Lr/2.