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Arc length is the distance along the curved line of a circle between two points. It depends on the radius and the central angle subtended by the arc.
Fórmula
s = rθ (θ in radians) or s = 2πr(θ°/360°) (θ in degrees)
- r
- radius (length)
- θ
- central angle (radians or degrees)
- s
- arc length (length)
Guía paso a paso
- 1Arc length = r × θ (where θ is in radians)
- 2Arc length = (θ/360) × 2πr (where θ is in degrees)
- 3Sector area = ½r²θ (radians)
- 4Convert degrees to radians: θ_rad = θ_deg × π/180
Ejemplos resueltos
Entrada
r = 5, θ = 90°
Resultado
Arc length = 5 × (π/2) ≈ 7.854
Entrada
r = 10, θ = 2 radians
Resultado
Arc length = 10 × 2 = 20
Preguntas frecuentes
Why is arc length different from chord length?
Arc length measures the actual curved path along the circle, while chord length is the straight-line distance between endpoints. The arc is always longer unless the angle is 0.
What is the arc length of a full circle?
For a full circle (θ = 360° = 2π rad), the arc length equals the circumference: s = 2πr.
How do I convert between degrees and radians for arc length?
Use the formula: θ_radians = θ_degrees × π/180, or θ_degrees = θ_radians × 180/π.
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