How to use this calculator
- Enter or choose i know.
- Enter or choose radius.
- Enter or choose length unit.
- The sector area updates as you type. Use Copy result or Share to keep it.
Method
Area = (θ/360°) × πr² = ½r²θ (θ in radians) = ½ × r × s; s = rθ
- r
- radius
- θ
- central angle
- s
- arc length
Worked example
- 90° is 90/360 = 25% of the circle.
- Area = 0.25 × π × 6² = 9π ≈ 28.274334 cm².
- Arc = 0.25 × 2π × 6 = 3π ≈ 9.424778 cm.
A quarter circle of radius 6 cm has an area of about 28.27 cm².
What the result means
Use it for pie-chart slices, fan-shaped rooms, sprinkler coverage or a slice of a round cake. Doubling the radius quadruples the area at the same angle.
Assumptions and limits
- The sector is cut from a perfect circle by two radii.
- The arc cannot be longer than the full circumference, and the angle cannot exceed 360°.
- For the area between the arc and its chord, use the segment area on the arc length calculator.
Questions
What is the difference between a sector and a segment?
A sector is bounded by two radii and the arc (a pie slice). A segment is bounded by a chord and the arc.