Area of a Sector Calculator
A sector is a pizza-slice part of a circle. Its area is the same fraction of πr² as its angle is of 360°.
A = (θ/360) × πr²
Perimeter: P = 2r + (θ/360) × 2πr
Area of the sector
18.8496ft²
- Perimeter
- 18.2832 ft
- Fraction of circle = 60 / 360 = 0.166667
- A = 0.166667 × π × 6² = 18.8496 ft²
- Arc = 6.2832 ft
Area in other units
| m² | 1.7512 |
| cm² | 17,511.8 |
| ft² | 18.8496 |
| in² | 2,714.34 |
| yd² | 2.0944 |
| acres | 0.000433 |
| hectares | 0.000175 |
How to find the area of a sector
Formula: A = (θ/360) × πr². Perimeter: P = 2r + (θ/360) × 2πr.
- Measure every length in the same unit. Mixing feet and inches is the most common mistake; convert first (6 in = 0.5 ft).
- Put the numbers into the formula above. The calculator shows each substitution with your numbers.
- Area comes out in square units (ft², m²). If you need a different unit, open "Area in other units".
Questions people ask
What is the area of a sector in radians?
A = ½ r² θ with θ in radians. A 1-radian sector of radius 6 has area 18.
How is a sector different from a segment?
A sector is bounded by two radii and an arc; a segment is bounded by a chord and an arc. The arc length calculator gives both.
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