Area of a Circular Sector Calculator
A = ½ r² θ (radians) or A = πr² × (θ/360) (degrees).
Result
Area
13.0900 units²
Arc length: 5.2360.
- Radius5
- Angle (rad)1.0472
- Angle (deg)60.0000
- Arc length5.2360
- Fraction of full circle16.67%
Step-by-step
- Convert to radians: 60° × π/180 = 1.0472.
- Area = ½ × r² × θ = ½ × 5² × 1.0472 = 13.0900.
How to use this calculator
- Enter the radius.
- Enter the central angle in degrees or radians.
- Read sector area and arc length.
About this calculator
A sector is a "slice" of a circle bounded by two radii and an arc. The area is a fraction of the full circle proportional to the central angle. In radians the formula is A = ½r²θ; in degrees it's A = πr² × (θ/360). Arc length is r × θ (radians).
Frequently asked
The radian formula ½r²θ works because radian = arc/radius is dimensionless. Degrees need a conversion factor (π/180).
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