Sector Area Calculator
Calculate sector area, arc length, and perimeter from radius and central angle
Enter angle between 0 and 360 degrees
Sector Formulas
Sector Area:
Area = (θ/360) × πr²
Where θ is the central angle in degrees and r is the radius
Example: (90/360) × π × 10² = 78.54 square units
Arc Length:
Arc = (θ/360) × 2πr
The curved distance along the sector edge
Example: (90/360) × 2π × 10 = 15.71 units
Sector Perimeter:
Perimeter = 2r + Arc Length
Sum of two radii plus the arc
Example: 2(10) + 15.71 = 35.71 units
History
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Pro Tips
- •A 90° sector is 1/4 of a full circle
- •180° creates a semicircle
- •Convert degrees to radians: multiply by π/180
- •Sectors are common in pie charts and graphs
- •Used in architecture and landscaping design
Common Angles
Frequently Asked Questions
What is a sector of a circle?
A sector is a portion of a circle bounded by two radii and the arc between them, like a slice of pie. The sector includes the area between the two radii and the curved arc. Common examples include pizza slices, pie charts, and angular measurements in technical drawings.
How do you calculate the area of a sector?
The sector area formula is: Area = (θ/360) × πr², where θ is the central angle in degrees and r is the radius. For example, a sector with a 90° angle and 10 cm radius has an area of (90/360) × π × 10² = 78.54 cm². In radians, use Area = (1/2) × r² × θ.
What is arc length and how is it calculated?
Arc length is the distance along the curved part of the sector. Calculate it using: Arc Length = (θ/360) × 2πr, where θ is in degrees. For a 60° sector with radius 12 cm: (60/360) × 2π × 12 = 12.57 cm. In radians: Arc Length = r × θ.
How do you find the perimeter of a sector?
The sector perimeter includes two radii plus the arc length: Perimeter = 2r + Arc Length. For example, with radius 8 cm and 45° angle: Perimeter = 2(8) + [(45/360) × 2π × 8] = 16 + 6.28 = 22.28 cm. This gives the total distance around the sector.
What Our Users Say
"This calculator is perfect for teaching circular geometry! My students use it to verify their homework and understand the relationships between radius, angle, and area. The visual charts really help them grasp the concepts."
"I use this daily for calculating curved garden beds and circular patio sections. The ability to quickly get area and perimeter measurements saves me tons of time on estimates. Highly accurate and reliable!"
"Great tool for geometry and trigonometry problems. The conversion between degrees and radians is super helpful, and I love that it shows all related measurements at once. Makes checking my work so much easier!"
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