Arc Length Calculator
Calculate arc length, sector area, chord length, and more from radius and angle.
Results
Arc Length
-
Circumference
-
Arc Percentage
-
Sector Area
-
Chord Length
-
Understanding Arc Length
An arc is a portion of the circumference of a circle. The arc length is the distance along the curved line making up the arc. To calculate arc length, you need to know the radius and the central angle.
Key Formulas
- Arc Length: L = r × θ (where θ is in radians)
- Sector Area: A = ½ × r² × θ (where θ is in radians)
- Chord Length: c = 2r × sin(θ/2)
- Circumference: C = 2Ï€r
- Arc Percentage: (θ / 2π) × 100%
Note: When working with arc length, angles must be in radians. To convert degrees to radians, multiply by π/180. For example, 90° = π/2 radians ≈ 1.5708 radians. This calculator handles the conversion automatically when you select degrees.
This calculator provides mathematical calculations for arc length, sector area, and related measurements based on standard geometric formulas. Results are accurate to four decimal places. While we strive for accuracy, please verify important calculations independently. This tool is for educational and informational purposes.