Sector Area Calculator
Calculate the area, arc length, and perimeter of a circle sector instantly.
Understanding the Area of a Sector
A sector is a portion of a circle enclosed by two radii and an arc. Think of it as a slice of pizza or a piece of pie. To calculate the properties of this "slice," you need two primary pieces of information: the radius of the circle and the central angle that defines the opening of the sector.
The Mathematical Formulas
Depending on whether your angle is measured in degrees or radians, the formula for the area changes slightly:
- Degrees: Area = (θ / 360) × π × r²
- Radians: Area = 0.5 × r² × θ
Where r is the radius and θ is the central angle.
Practical Examples
| Radius (r) | Angle (θ) | Unit | Calculated Area |
|---|---|---|---|
| 5 cm | 90° | Degrees | 19.63 cm² |
| 10 m | π/2 (1.57) | Radians | 78.54 m² |
| 12 in | 45° | Degrees | 56.55 in² |
How to use this Calculator
1. Enter the Radius of your circle. This is the distance from the center to the edge.
2. Select your Angle Unit. Most geometry problems use degrees, but advanced physics or calculus often uses radians.
3. Input the Central Angle. If you are using degrees, a full circle is 360°. If using radians, a full circle is 2π (approx 6.283).
4. Click Calculate to see the total area, the length of the curved arc, and the total perimeter (which includes the two straight radii and the curved arc).