Area of a Sector Calculator
An Area of a Sector Calculator helps you quickly find the area of a sector of a circle when you know the circle's radius and the central angle. A sector is the portion of a circle enclosed by two radii and the arc between them. This calculator is useful for geometry problems, mathematics homework, engineering calculations, and everyday measurements.
What Is the Area of a Sector?
A sector can be thought of as a slice of a circular shape, similar to a piece of pie. The size of the sector depends on the radius of the circle and the angle at its center. A larger central angle represents a larger portion of the circle and therefore has a greater area.
Area of a Sector Formula
When the central angle is measured in degrees, the area of a sector can be calculated using:
Area = (θ / 360) × π × r²
Where:
- Area = area of the sector
- θ = central angle in degrees
- r = radius of the circle
- π ≈ 3.14159
Example Calculation
Suppose a circle has a radius of 10 cm and the sector has a central angle of 90°.
Area = (90 / 360) × π × 10²
Area = 25π ≈ 78.54 cm²
Therefore, the area of the sector is approximately 78.54 square centimeters.
How to Use the Area of a Sector Calculator
- Enter the radius of the circle.
- Enter the central angle of the sector.
- Select the appropriate units if available.
- Click the calculate button.
- Review the calculated area of the sector.
Make sure the angle is entered in degrees when using the standard sector-area formula shown above.
Sector Area vs. Circle Area
The area of a complete circle is πr². A sector represents only part of that circle. The fraction of the circle represented by the sector is determined by its central angle. For example, a 180° sector covers half of a circle, while a 90° sector covers one-quarter of the circle.
Where Is the Area of a Sector Used?
Sector-area calculations are commonly used in geometry, construction, architecture, engineering, landscaping, and design. They can also be useful when calculating the area of curved sections, circular gardens, fan-shaped spaces, or other parts of a circle.
Related Calculators
You may also find our Circumference Calculator useful when working with circles. For other mathematical calculations, you can explore our Math Calculators.
Frequently Asked Questions
What is a sector of a circle?
A sector is a part of a circle enclosed by two radii and the arc connecting their endpoints.
What formula is used to calculate the area of a sector?
For an angle measured in degrees, the formula is Area = (θ / 360) × π × r².
Can I calculate the area of a sector without knowing the diameter?
Yes. You only need the radius and central angle. If you know the diameter, divide it by 2 to obtain the radius.
What units are used for sector area?
The result is expressed in square units. For example, if the radius is measured in centimeters, the area will be in square centimeters (cm²).
Final Thoughts
The Area of a Sector Calculator makes circular-area calculations faster and easier. By entering the radius and central angle, you can quickly determine the area of a specific section of a circle without performing the formula manually. For accurate results, always check that your measurements use the correct units and that the angle is entered correctly.