Circle Sector Calculator
Calculate the area, arc length, chord length, and perimeter of a circle sector.
How it works
- 1Enter the circle’s radius and the central angle in degrees. The sector is the pie-slice region bounded by two radii and the arc between them.
- 2Area is computed as ½r²θ where θ is the central angle in radians, giving the exact portion of the full circle’s area.
- 3Arc length equals r·θ; chord length is 2r·sin(θ÷2); perimeter adds the arc to both straight radii.
Use cases
- Engineering and architecture: calculate material for curved panels, pipes, or arched openings defined by a radius and sweep angle.
- Education: verify geometry homework involving sectors, arc lengths, and circle theorems.
- Design and fabrication: determine the exact arc length needed when bending sheet metal or cutting circular segments.
Frequently asked questions
What is a circle sector?
A sector is a pie-slice region of a circle formed by two radii and the arc they subtend. Its size is set by the central angle θ between the two radii.
How is sector area calculated?
Area = ½r²θ, where r is the radius and θ is the central angle in radians. For a full circle (θ = 2π) this reduces to πr².
What is the difference between arc length and chord length?
Arc length is the curved distance along the circle’s edge (r·θ). Chord length is the straight-line distance between the two endpoints (2r·sin(θ÷2)).
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