Arc Length Calculator

Step-by-Step Calculation:

1. Identify the radius (r) - Distance from center to edge
2. Identify the central angle (θ) - Angle at the center of the circle
3. Convert angle to radians (if in degrees): θ(rad) = θ(deg) × π/180
4. Apply the formula: Arc Length = r × θ(rad)
5. Include units - Same units as the radius

Alternative Formulas:

• Using Diameter: Arc Length = (d × θ × π) / 360° (θ in degrees)
• Using Circumference: Arc Length = (C × θ) / 360° (θ in degrees)
• Fraction of Circle: Arc Length = (θ/360°) × 2πr (θ in degrees)

Real-World Applications:

• Engineering: Designing curved roads, bridges, and structures
• Architecture: Calculating materials for curved walls and arches
• Manufacturing: Cutting curved materials and components
• Navigation: Calculating distances along curved paths
• Sports: Track design and field measurements

Common Angle Conversions:

• 90° = π/2 radians ≈ 1.5708 radians
• 180° = π radians ≈ 3.1416 radians
• 270° = 3π/2 radians ≈ 4.7124 radians
• 360° = 2π radians ≈ 6.2832 radians