Sector Area Calculator

What is a Sector Area Calculator?

A Sector Area Calculator is a tool used to determine the area of a sector of a circle. A sector is a part of a circle enclosed by two radii and the arc connecting them, much like a slice of a pie. This calculator typically requires the radius of the circle and the central angle of the sector (in degrees or radians) to compute the area.

Understanding the area of a sector is important in various fields, including geometry, engineering, design, and physics. For example, it can be used to calculate the area of a circular land plot segment, the surface area of a component in a machine, or the region covered by a radar sweep.

Sector Area Formulas

The area of a sector can be calculated using one of two primary formulas, depending on whether the central angle is given in degrees or radians.

If the angle θ is in degrees:

Area = (θ / 360) * π * r²

If the angle θ is in radians:

Area = (1/2) * r² * θ

Where:

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

How to Calculate Sector Area: Example

Let's calculate the area of a sector with a radius of 7 units and a central angle of 60 degrees.

1. Identify the radius (r): r = 7 units.
2. Identify the central angle (θ) in degrees: θ = 60°.
3. Apply the formula for degrees: Area = (θ / 360) * π * r²
4. Substitute the values: Area = (60 / 360) * π * (7)²
5. Calculate: Area = (1/6) * π * 49 ≈ (1/6) * 3.14159 * 49 ≈ 25.66 square units.

If the angle was given in radians, say π/3 radians (which is 60°):

1. Radius (r): r = 7 units.
2. Central angle (θ) in radians: θ = π/3.
3. Apply the formula for radians: Area = (1/2) * r² * θ
4. Substitute: Area = (1/2) * (7)² * (π/3) = (1/2) * 49 * (π/3) = 49π / 6.
5. Calculate: Area ≈ 49 * 3.14159 / 6 ≈ 25.66 square units.

Common Applications

• Architecture and Construction: Designing curved structures, rooms, or features.
• Land Surveying: Calculating the area of pie-shaped land parcels.
• Engineering: Determining the surface area of parts of cylindrical objects or the cross-sectional area of pipes with partial flow.
• Graphic Design: Creating circular charts, diagrams, or logos with specific segment areas.
• Physics: Calculating quantities related to circular motion or fields spreading in a sector.