Arc length

Math

Definition

The distance along a curved line. In calculus, the arc length of y = f(x) from x = a to x = b is found by integrating √(1 + [f′(x)]²) dx. In a circle, arc length equals the radius times the central angle in radians.

Examples

  • The arc length of a 60° (π/3 radian) arc on a circle of radius 6 is 6 · π/3 = 2π
  • Finding the length of y = x^(3/2) from x = 0 to x = 4 using the calculus formula
Key Fact

Circle: s = rθ; Calculus: L = ∫ from a to b √(1 + [f′(x)]²) dx

Related Terms

Arc length and sector area Degree to radian conversion Central and inscribed angles Circles and circumference

Study This Concept

Practice arc length with free review games in these units:

Geometry Unit 9: Circles