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How It Works
A sector is a “pie slice” of a circle bounded by two radii and the arc between them. The sector area formula A = ½r²θ uses the central angle in radians. If you know the angle in degrees, the calculator converts it automatically.
You can solve for any of the three variables: the area, the radius, or the central angle. Enter the two known values and click Calculate.
Example Problem
A sector has a radius of 5 and a central angle of 90°. Find the sector area.
- Convert 90° to radians: 90 × π/180 = π/2 ≈ 1.5708 rad
- A = ½ × 5² × 1.5708 = ½ × 25 × 1.5708 ≈ 19.635
The sector area is approximately 19.635 square units, which is one-quarter of the full circle area (π×25 ≈ 78.54).
Frequently Asked Questions
What is the formula for sector area?
The sector area is A = ½r²θ, where r is the radius and θ is the central angle in radians. For degrees, use A = (θ/360)πr².
How do you convert degrees to radians?
Multiply the degree measure by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 radians. A full circle is 360° = 2π radians.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc (a pie slice). A segment is bounded by a chord and an arc. The segment area equals the sector area minus the triangle formed by the two radii and chord.
What fraction of a circle is a 60-degree sector?
A 60-degree sector is 60/360 = 1/6 of the full circle. Its area is one-sixth of πr². For a radius of 6, the sector area is ½×36×(π/3) ≈ 18.85 square units.
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- Angle Converter — Convert between degrees, radians, and gradians.
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