🧮 Arc Length Calculator

🌟 Arc Length Calculator

Calculate arc length with radius and angle measurements

Results

Results

Results

Results

Results

Results

Visual Representation

🎓 Arc Length Theory

An arc length is the distance along the curved line making up the arc. It's a portion of the circumference of a circle.

Basic Formula:
Arc Length = r × θ (when θ is in radians)
Arc Length = (r × θ × π) / 180° (when θ is in degrees)

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