Arc length and sector area

Math

Definition

Arc length is the distance along a circular arc, calculated as s = rθ where θ is in radians. Sector area is the area of the 'pie slice' region, calculated as A = ½r²θ. Both formulas require the angle to be in radians.

Examples

  • A sector with radius 10 cm and central angle of π/4 radians has arc length 10·π/4 ≈ 7.85 cm and area ½·100·π/4 ≈ 39.27 cm²
  • Finding how much pizza crust is on a slice that subtends a 45° angle from a 14-inch diameter pizza
Key Fact

Arc length: s = rθ, Sector area: A = ½r²θ (θ in radians)

Related Terms

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

Study This Concept

Practice arc length and sector area with free review games in these units:

Trigonometry Unit 1: Angles and Radian Measure