Just enter the Radius and the Central Angle of the circular sector below and click Calculate Area. Use a period or comma as the decimal separator.
Circular Sector Area Calculator
Result:
Circular sector area formula
The area of a circular sector is calculated proportionally to the central angle relative to the full circle (360°):
A = (θ ÷ 360) × π × r²
Where θ is the central angle in degrees and r is the radius. When θ = 360°, the circular sector is the full circle, and the formula reduces to A = π × r².
Practical examples
| Radius (r) | Angle (θ) | Area (A = (θ ÷ 360) × π × r²) |
|---|---|---|
| 8 m | 90° | 50.265 m² |
| 10 cm | 120° | 104.720 cm² |
| 5 m | 180° | 39.270 m² |
| 6 cm | 60° | 18.850 cm² |
| 4 m | 270° | 37.699 m² |
Frequently asked questions
What is a circular sector?
A circular sector is the region of a circle bounded by two radii and the arc between them, similar to a slice of pizza. The angle between the radii is called the central angle.
What is the formula for the area of a circular sector?
The area is A = (θ ÷ 360) × π × r². Example: r = 8 m and θ = 90° → A = (90 ÷ 360) × π × 64 = 0.25 × π × 64 ≈ 50.265 m².
What is the central angle of a circular sector?
The central angle is the angle formed by the two radii that bound the sector. It can range from 0° (exclusive) to 360° (full circle). A 90° pizza slice represents a quarter of the circle.
Can I use a comma instead of a decimal point?
Yes. This calculator accepts both a comma and a period as the decimal separator.
See also…
