Sector of a Circle Formulas
2D Shapes
Sector of a Circle
- Area
- A = (θ ⁄ 360°) × πr2
- Arc length
- L = (θ ⁄ 360°) × 2πr
- r radius
- θ central angle in degrees
Sector of a Circle formulas explained
A sector is a “pizza slice” of a circle bounded by two radii and an arc. Its share of the circle equals θ ⁄ 360°. Below are all the sector of a circle formulas with what each letter means, a worked example and a free calculator.
- Area:
A = (θ ⁄ 360°) × πr² - Arc length:
L = (θ ⁄ 360°) × 2πr
Sector of a Circle calculator
Live calculator
Sector of a Circle calculator
Worked example: area of a sector of a circle
Given Radius r = 10 cm, Angle θ (°) = 60 cm, substitute the values into each sector of a circle formula:
- A = (60 ⁄ 360) × π × 10² = 52.36 cm²
- L = (60 ⁄ 360) × 2π × 10 = 10.47 cm
Sector of a Circle Formula SheetFormulas, variables, a worked example and practice questions with answers.Download PDFOpen
Sector of a Circle formulas FAQ
What is the formula for the area of a sector of a circle?
The area of a sector of a circle is A = (θ ⁄ 360°) × πr², where r is the radius, θ is the central angle in degrees.
What is the formula for the arc length of a sector of a circle?
The arc length of a sector of a circle is L = (θ ⁄ 360°) × 2πr, where r is the radius, θ is the central angle in degrees.
Can I download the sector of a circle formulas as a PDF?
Yes. Use the Download PDF button on this page for a free printable sector of a circle formula sheet with a worked example and practice questions.
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