Sector Area Calculator
Find the area of a sector of a circle from its radius and central angle in degrees or radians, with the arc length and chord.
Sector area
78.539816
- Arc length
- 15.707963
- Chord length
- 14.142136
- Perimeter of the sector
- 35.707963
- Share of the whole circle
- 25%
The sector covers an area of 78.5398 square units.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Sector area | 90 ÷ 360 × π × 10² | 78.539816 |
| Arc length | 10 × 1.5708 radians | 15.707963 |
How it works
Enter the radius and the central angle, and choose degrees or radians.
Worked example
A sector with radius 10 and a 90° angle:
- Area: 90 ÷ 360 × π × 10² = 78.5398
- Arc length: 10 × (π ÷ 2) = 15.708
- Chord: 2 × 10 × sin(45°) = 14.1421
Sources
Frequently asked questions
What is the formula for the area of a sector?
With the angle in degrees, the area is the angle divided by 360, times πr². With the angle in radians it is one half of r² times the angle. A 90° sector of a circle with radius 10 has an area of 78.54.
What is a sector of a circle?
A sector is the slice of a circle between two radii, like a slice of pizza. The angle between the two radii is the central angle.
How do I convert degrees to radians?
Multiply by π and divide by 180. A right angle of 90° is π/2 radians, about 1.5708, and a full turn of 360° is 2π radians.
How do I find the arc length of the sector?
Multiply the radius by the angle in radians, s = rθ. The calculator shows it, along with the chord and the perimeter of the sector. For more arc problems, use the arc length calculator.
Can the angle be more than 360 degrees?
No. A sector cannot cover more than the whole circle, so the angle must be above 0 and at most 360 degrees, or 2π radians.