Sector Area Calculator
Calculate the area of a circular sector (like a pizza slice) using radius and central angle. Supports both degrees and radians.
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Frequently Asked Questions
What is a sector of a circle?
A sector is the region bounded by two radii and the arc between them. It looks like a pizza slice or a pie wedge.
What is the formula for sector area?
A = ½r²θ (when θ is in radians), or A = (θ/360°) × πr² (when θ is in degrees), where A is sector area, r is radius, and θ is the central angle.
How is sector area different from segment area?
A sector includes the two radii (like a pizza slice), while a segment is just the area between the chord and the arc (without the radii extending to the center).
What is the sector area for 90 degrees?
For a 90° angle (quarter circle), the sector area is πr²/4, which is exactly one-fourth of the full circle's area.
What is the sector area for 180 degrees?
For a 180° angle (semicircle), the sector area is πr²/2, which is exactly half of the full circle's area.
Can sector area be greater than circle area?
No, a sector is always part of a circle, so its area cannot exceed the total circle area πr². The maximum sector area equals the full circle when θ = 360° or 2π radians.
How do you find the central angle from sector area?
Rearrange the formula: θ = 2A/r² (in radians) or θ = 360A/(πr²) (in degrees).
Where are sector calculations used?
Sector calculations are used in pie charts, pizza and cake portions, fan blade design, radar coverage areas, and many geometric applications.