Sector Area Calculator
Calculate the area of a circle sector in multiple ways: from radius and angle (deg or rad), from diameter, or from arc length. You also get arc length, sector perimeter, central angle in both degrees and radians, and the sector’s percentage of the full circle.
same unit for all
central angle
Sector formulas used
Area from degrees: \( A = \frac{\theta}{360^\circ} \cdot \pi r^2 \)
Area from radians: \( A = \frac{1}{2} r^2 \theta \)
Arc length (deg): \( L = \frac{\theta}{360^\circ} \cdot 2 \pi r \)
Arc length (rad): \( L = r \theta \)
From arc length and radius: \( \theta = \frac{L}{r} \) (rad), then \( A = \frac{1}{2} r L \)
Sector perimeter: \( P = 2r + L \)
FAQs
What units does this calculator support?
Any length unit: cm, m, in, ft — just be consistent. Area will be in the squared version of that unit.
What’s the fastest way if I only know the arc length?
Use the “Arc length + Radius” tab; it computes the angle automatically and then the area.
What if I want semicircle or quarter circle?
Use the % tab: 50% → semicircle, 25% → quarter circle, 12.5% → 45° sector.
Formula (LaTeX) + variables + units
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Area from degrees: \( A = \frac{\theta}{360^\circ} \cdot \pi r^2 \) Area from radians: \( A = \frac{1}{2} r^2 \theta \) Arc length (deg): \( L = \frac{\theta}{360^\circ} \cdot 2 \pi r \) Arc length (rad): \( L = r \theta \) From arc length and radius: \( \theta = \frac{L}{r} \) (rad), then \( A = \frac{1}{2} r L \) Sector perimeter: \( P = 2r + L \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.