Sector Area Calculator
A circular sector is a region of a circle bounded by two radii and the arc that connects them, resembling a slice of pie. This calculator determines the area and arc length of a circular sector given the radius and the central angle. The central angle can be entered in either degrees or radians. The area formula uses the angle in radians and is Area = (1/2) * r^2 * theta. The arc length is calculated as Arc length = r * theta in radians. This calculator automatically performs conversions and displays results for both degree and radian measurements.
Sector formulas
Area = (1/2) * r^2 * theta (theta in radians)
Area = (r^2 * theta * pi) / 360 (theta in degrees)
Arc length = r * theta (theta in radians)
Arc length = (r * theta * pi) / 180 (theta in degrees)
Perimeter = arc length + 2 * r
Example calculation
For a sector with radius 10 and central angle of 45 degrees (0.785 radians):
- Area = (1/2) * 10^2 * 0.785 = (1/2) * 100 * 0.785 = 39.27 square units
- Arc length = 10 * 0.785 = 7.85 units
- Perimeter = 7.85 + 2 * 10 = 27.85 units
Sector area calculator: frequently asked questions
What is a circular sector?
A circular sector is the region of a circle that is bounded by two radii and the arc between them. It looks like a slice of pie. The angle at the center is called the central angle.
What is the formula for the area of a sector?
The area of a sector is calculated using the central angle in radians: Area = (1/2) * r^2 * theta. When using degrees, the formula is: Area = (r^2 * theta * pi) / 360, where theta is in degrees.
What is the arc length of a sector?
The arc length is the curved part of the sector boundary. It is calculated as: Arc length = r * theta, where theta is in radians. In degrees: Arc length = (r * theta * pi) / 180.
How do I convert between degrees and radians?
To convert degrees to radians, multiply by pi and divide by 180: radians = degrees * pi / 180. To convert radians to degrees, multiply by 180 and divide by pi: degrees = radians * 180 / pi.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc. A segment is bounded by a chord and an arc (the area between a chord and the arc). A sector includes the central angle, while a segment does not.
Official sources
- Wolfram MathWorld: Circular Sector.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.