Arc Length & Sector Area Calculator
Compute the arc length and sector area of a circle from radius and central angle.
Inputs
Arc = rθ, Sector area = ½r²θ (θ in radians)
Results
Enter values and click calculate.
Formulas
• Arc length: s = r · θ (θ in radians)
• Sector area: A = ½ · r² · θ (θ in radians)
• In degrees: s = (θ/360) · 2πr; A = (θ/360) · πr²
Frequently Asked Questions
What is arc length?▾
The distance along the curved edge of a circle between two endpoints. For a central angle θ in radians, arc length s = r·θ.
What is sector area?▾
The area of a "pie slice" bounded by two radii and an arc. For θ in radians, A = ½·r²·θ.
How do degree formulas differ?▾
Arc length: s = (θ/360)·2πr. Sector area: A = (θ/360)·πr². Both convert the degree fraction to a radian one before multiplying.
Why do the formulas use radians?▾
Radians are defined so that arc length on a unit circle equals the angle. That definition makes the formulas linear and clean.