Sector Area Calculator

Understanding and Calculating the Area of a Sector

A sector is a portion of a circle that is enclosed by two radii and an arc. It resembles a “slice of pie” or “pizza slice.” The area of a sector is a fraction of the total area of the circle, determined by the central angle of the sector.
Formula for Sector Area

The area A of a sector can be calculated using the following formula:

$$ \text{Area} = \frac{A}{360} \times \pi r^2 $$

Where:

• r is the radius of the circle.
• A is the central angle of the sector in degrees.
• π (pi) is a mathematical constant approximately equal to 3.14159.

Step-by-Step Calculation

Measure the Radius:

Determine the radius r of the circle. The radius is the distance from the center of the circle to any point on its edge.

Measure the Central Angle:

Determine the central angle A of the sector in degrees. This is the angle formed between the two radii that enclose the sector.

Ensure the Validity of Inputs:

Verify that both the radius r and the central angle A are positive numbers.

Apply the Formula:

Use the formula to calculate the area of the sector.

$$ \text{Area} = \frac{A}{360} \times \pi r^2 $$

Example Calculation

Let’s calculate the area of a sector with a radius (r) of 30 meters and a central angle (A) of 90 degrees.

Conclusion

Calculating the area of a sector involves straightforward steps once you have the radius and the central angle. This calculation is useful in various applications, such as determining the area of a slice of land, a section of a circular object, or even a slice of pie. By understanding the formula and how to apply it, you can easily find the area of any sector.