Sector Area Calculator
Find the area, arc length, and perimeter of a circular sector from its radius and central angle. Works in degrees and radians.
Last updated:
Input
Enter the radius and central angle to compute the sector area, arc length, and perimeter.
Angle unit
Degrees
Result
Area
19.634954
Arc length
7.853982
Perimeter
17.853982
Lengths use the same unit as the input, and the area uses that unit squared.
How it works
- The area of a circular sector with radius r and central angle θ in radians is area = (1/2) × r² × θ.
- When the angle is given in degrees, this equals area = π × r² × (degrees ÷ 360).
- The arc length equals arc = r × θ where θ is in radians.
- The perimeter equals the arc length plus two radii (2r).
- The radius must be positive and the central angle must be greater than 0 and at most a full turn (360 degrees or 2π).
Frequently asked questions
- How do I calculate the area of a sector?
- With radius r and central angle θ in radians, the area is (1/2) × r² × θ. In degrees this is equivalent to π × r² × (angle ÷ 360).
- What happens if the central angle is 360 degrees?
- At 360 degrees (2π) the sector becomes a full circle, so the area equals πr². This calculator accepts any central angle greater than 0 and up to one full turn.
- Does it also give the arc length and perimeter?
- Yes. The arc length is r × θ (in radians), and the perimeter is that arc length plus two radii (2r).
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