Sector Area Calculator
A sector is a slice of a circle, bounded by two radii and the arc between them — a piece of pie. Enter the radius and the central angle to get its area, arc length and perimeter, plus the area of the segment cut off by the chord.
- Arc length
- 6.28 in
- Sector perimeter
- 18.28 in
- Segment area
- 3.26 in²
- Share of the full circle
- 16.67%
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Formula
How to use it
- Enter the radius and its unit.
- Enter the central angle in degrees or radians.
- Read the sector area and, if you need them, the arc, perimeter and segment.
Worked examples
A 60° sector with a 6-inch radius: 18.85 in², which is 0.01216 m²
- Sector area
- 18.85 in²
- Arc length
- 6.28 in
- Sector perimeter
- 18.28 in
- Segment area
- 3.26 in²
- Share of the full circle
- 16.67%
A 120° sector with a 3 m radius
- Sector area
- 9.42 m²
- Arc length
- 6.28 m
- Sector perimeter
- 12.28 m
- Segment area
- 5.53 m²
- Share of the full circle
- 33.33%
Sector or segment
A sector reaches the center of the circle, like a pizza slice. A segment is the part between a chord and the arc, like the piece cut off by a straight knife stroke. The segment equals the sector minus the triangle formed by the two radii and the chord.
Questions people ask
What is the area of a 60° sector with a radius of 6?
One sixth of the circle: (60 ÷ 360) × π × 36 = 18.85 square units.
What is the area of one slice of a 14-inch pizza cut into 8?
Each slice is a 45° sector with a 7-inch radius: (45 ÷ 360) × π × 49 = 19.24 square inches.
What share of a circle is a 120° sector?
One third, or 33.33%, because 120 ÷ 360 = ⅓.