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Sectors

Sectors: Arc Length & Area

Work with central angle θ in degrees or radians; compute arc length and sector area accurately.

Formulas (Degrees)

Arc length

L = (θ°/360°) × 2πr

Sector area

S = (θ°/360°) × πr²

Formulas (Radians)

Arc length

L = rθ

Sector area

S = ½r²θ

Common Pitfalls

  • • Using 360/θ instead of θ/360 for proportions.
  • • Mixing degrees in radian formulas without conversion.
  • • Forgetting to square r in sector area.

Practice & Tools

Sector Calculator

Compute arc length and area by radius and angle.

  • Method: L = rθ, S = ½r²θ (radians); proportions with θ°/360° (degrees)
  • Related: degree–radian conversion, central angle–arc relation
Open Sector Calculator

Practice Problems

Target common traps on angle conversions and formulas.

Go to Practice