Sector Area and Arc Length Calculator: Circles
Calculate the area of a circular sector and the length of an arc given the radius and central angle. Essential for geometry, engineering design, and circular moti...
Circular Sector Formulas
A circular sector is a "pie slice" portion of a circle defined by two radii and an arc. Its area and arc length depend on the radius and central angle. These calculations appear in engineering (gear design, cam profiles), architecture (arched structures), and physics (circular motion).
🥧 Sector Area & Arc Length Calculator
Free calculator for instant results.
📐 Formula
Arc = rθ | Area = ½r²θ
θ in radians. In degrees: Arc = (θ/360)×2πr | Area = (θ/360)×πr². For full circle (θ=2π): arc=2πr (circumference), area=πr².
📝 Worked Example
Sector: r=10m, θ=60°=π/3 rad:
Arc length = 10 × π/3 = 10.47 m
Area = ½ × 100 × π/3 = 52.36 m²
📝 How to Use
❓ FAQ
What is the difference between arc and chord?
Arc is the curved portion of the circle perimeter. Chord is the straight line joining the two endpoints. Arc ≥ Chord, with equality only when θ=0.
How is arc length used in circular motion?
Distance traveled by a point on a circle: s = rθ (θ in rad). Velocity v = rω, giving the connection between angular and linear motion.
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.