Area of a Sector Calculator
The area of a sector is the fraction of the circle it covers times πr²: a 60° sector of a 6 cm radius circle is 18.8496 cm².
18.8495559215388 cm²
Full answer, then cut to fewer decimals (not rounded):
- 18.8495559215388 cm²
- 18.849555921538 cm²
- 18.84955592153 cm²
- 18.8495559215 cm²
- 18.849555921 cm²
- 18.84955592 cm²
- 18.8495559 cm²
- 18.849555 cm²
- 18.84955 cm²
- 18.8495 cm²
- 18.849 cm²
- 18.84 cm²
- 18.8 cm²
- Area
- 18.8496 cm²
- Arc length
- 6.28319 cm
- Perimeter
- 18.2832 cm
In other units: 0.00188496 m² · 1884.96 mm² · 1.88496 × 10⁻⁹ km² · 1.88496 × 10⁻⁷ ha · 0.0202895 ft² · 2.92169 in² · 0.00225439 yd² · 4.65783 × 10⁻⁷ ac · 7.27785 × 10⁻¹⁰ mi²
Step-by-step solution
- A = (θ ÷ 360°) × π r²
- A = (60 ÷ 360) × π × 6² = 18.8496 cm²
Area of a Sector Formula
A = (θ ÷ 360°) π r² = ½ r² θ
r radius, θ central angle (degrees, or radians in ½r²θ)
Worked Example
A 60° sector of a 6 cm radius circle:
- A = (θ ÷ 360°) × π r²
- A = (60 ÷ 360) × π × 6² = 18.8496 cm²
Arc length: 6.28319 cm · Perimeter: 18.2832 cm
Same area in other units: 0.00188496 m² · 1884.96 mm² · 1.88496 × 10⁻⁹ km² · 1.88496 × 10⁻⁷ ha · 0.0202895 ft²
Frequently asked questions
What is the formula for the area of a sector in radians?
A = ½ r² θ, with θ in radians. A full circle (θ = 2π) gives πr², as expected.
How do I find the area of a sector from the arc length?
A = ½ × r × L. A sector with radius 6 cm and a 6.283 cm arc has an area of 18.85 cm².
How do I find the area of a segment?
Subtract the triangle from the sector: segment = ½ r² (θ − sin θ), with θ in radians.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Area of a Sector Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/area-of-a-sector/
IEEE
Scientific Converters, "Area of a Sector Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/area-of-a-sector/