Sector Area Calculator
Calculate the area of a circular sector from radius and angle.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Sector Area Calculator
This calculator finds the area of a circular sector, the "pie slice" shaped region bounded by two radii and an arc.
- Enter the radius. Type the radius of the circle.
- Enter the central angle. Type the angle that defines the sector.
- Choose the angle unit. Select degrees or radians from the dropdown.
- Read the result. The sector area and arc length appear with the formula used.
The formula in radians is A = 0.5 * r^2 * theta. In degrees, it is A = (theta/360) * pi * r^2. A sector with a 90-degree angle is one quarter of the full circle's area. Results update live as you type.
About Sector Area
A sector is a region of a circle enclosed by two radii and the arc between them. Think of it as a slice of a pie or pizza. The sector area is proportional to the central angle: a larger angle means a larger fraction of the full circle. At 360 degrees (or 2*pi radians), the sector area equals the full circle area. Sector area calculations are used in engineering for gear teeth, in construction for curved walls and arches, in data visualization for pie charts, and in physics for rotational work and torque calculations.
Frequently Asked Questions
What is the formula for sector area?
In radians: A = 0.5 * r^2 * theta. In degrees: A = (theta/360) * pi * r^2. Both give the same result. For a circle with radius 10 and a 90-degree angle, the sector area is (90/360) * pi * 100 = 78.5398 / 4 = 25*pi, approximately 78.54.
What is the difference between sector area and arc length?
Sector area is the two-dimensional space inside the sector (measured in square units). Arc length is the one-dimensional distance along the curved edge of the sector (measured in linear units). Both depend on the radius and angle.
What angle gives half the circle's area?
A central angle of 180 degrees (or pi radians) creates a semicircle, which is exactly half the circle's area. Similarly, 90 degrees gives a quarter, and 120 degrees gives a third.