Sector Area CalculatorFree online math calculator — instant results, no sign-up
Calculate a circular sector's area from its central angle.
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About the Sector Area Calculator
The Sector Area Calculator finds the area of a circular sector from its radius and central angle in degrees. It treats the sector as a fraction of the full circle, using the angle divided by 360. With the default radius of 5 and central angle of 60°, the result is 13.08996939 square units.
- Radius
- The radius is the distance from the circle’s center to its edge, measured in a length unit such as centimeters or meters; the default is 5.
- Central angle (degrees)
- The central angle is the angle between the two radii bounding the sector, measured in degrees; the default is 60.
Formula and method
A = (θ / 360) × π × r²; with the default inputs, A = (60 / 360) × π × 5² = 25π / 6 ≈ 13.08996939.
- AThe sector’s area, in square units corresponding to the radius unit.
- rThe circle’s radius, in length units.
- θThe sector’s central angle, expressed in degrees.
- πPi, the ratio of a circle’s circumference to its diameter.
Square the radius and multiply by π to find the full circle’s area. Divide the central angle in degrees by 360 to find the fraction of the circle occupied by the sector, then multiply that fraction by the circle’s area. For r = 5 and θ = 60°, the fraction is 1/6 and the sector area is 25π/6, which rounds to 13.08996939.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Radius5
- Central angle (degrees)60
Results
- Result13.08996939
How to use the Sector Area Calculator
- 1Enter the circle’s radius in the Radius field; keep 5 to reproduce the default example.
- 2Enter the sector’s angle in Central angle (degrees); keep 60 for the default example.
- 3Check that the angle is in degrees, not radians, and that the radius is nonnegative.
- 4Run the calculation to apply A = (θ / 360) × π × r².
- 5Read the Result as the sector’s area: the default inputs give 13.08996939 square units.
Reading your result
The Result row reports the area enclosed by the two bounding radii and the circular arc. For radius 5 and central angle 60°, Result = 13.08996939, representing one-sixth of the full circle’s area. The output unit is the square of the radius unit: a radius entered in centimeters produces an area in square centimeters.
Limitations
The formula assumes a flat, circular sector with a constant radius and an angle measured at the circle’s center. For an ordinary sector, use a nonnegative radius and an angle from 0° to 360°; angles outside that range do not describe a single ordinary sector. The tool does not calculate a circular segment, which is bounded by a chord and an arc, or an annular sector between two circles. The displayed decimal is rounded, and the accuracy of a measured area depends on the accuracy of the inputs.
Common questions
Why does the formula divide the central angle by 360?+
A full circle spans 360°, so θ/360 is the fraction of its area contained in the sector. With the default angle of 60°, the sector occupies 1/6 of the circle.
Can I enter a central angle in radians?+
Not directly: this input expects degrees. Convert radians to degrees using θ = radians × 180/π before entering the angle.
Does this calculator find the area between a chord and an arc?+
No. That region is a circular segment. This calculator finds a sector, whose straight boundaries are two radii meeting at the circle’s center.
Can I calculate a sector larger than a semicircle?+
Yes. Enter the sector’s actual central angle between 180° and 360°. Use the larger angle for a major sector rather than the smaller angle between its bounding radii.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.