Sector Area Calculator

How to Calculate Sector Area

A sector is a part of a circular disk enclosed by two radii and an arc. Calculating its area is a common problem in geometry with practical applications in various fields.

Sector Area Formula

The formula for calculating the area of a sector is:

\(A = \frac{\theta}{360°} \pi r^2\)

Where:

• \(A\) is the area of the sector
• \(\theta\) is the central angle in degrees
• \(r\) is the radius of the circle

Calculation Steps

1. Identify the central angle (\(\theta\)) in degrees and the radius (\(r\)) of the circle.
2. Substitute these values into the formula: \(A = \frac{\theta}{360°} \pi r^2\)
3. Calculate the result, typically leaving it in terms of \(\pi\) for exact values or using 3.14159 for approximate results.

Example Calculation

Let's calculate the area of a sector with a central angle of 45° and a radius of 10 units:

1. Given: \(\theta = 45°\), \(r = 10\) units
2. Substitute into the formula: \(A = \frac{45°}{360°} \pi (10)^2\)
3. Simplify: \(A = \frac{1}{8} \pi (100) = 12.5\pi\) square units
4. For an approximate value: \(A \approx 12.5 \times 3.14159 \approx 39.27\) square units

Visual Representation

This diagram illustrates a sector with central angle θ and radius r. The sector is shown in blue, while the radii defining the sector are drawn in red. The central angle θ is measured at the center of the circle, and the radius r extends from the center to any point on the circle's circumference.