Sector Area Calculator

This calculator helps you find the area of a sector of a circle, ideal for students, engineers, and professionals dealing with geometric calculations. Enter the radius and the angle to get the sector area instantly.

Calculate Sector Area

Radius (r) *

Angle (θ in degrees) *

Results

Sector Area: 0

Data Source and Methodology

All calculations are strictly based on the mathematical formula for the area of a sector. Consult Math is Fun for more details. All calculations use the formula: \( \text{Area} = \frac{\theta}{360} \times \pi \times r^2 \).

The Formula Explained

\[ \text{Area} = \frac{\theta}{360} \times \pi \times r^2 \]

Glossary of Terms

Radius (r): The distance from the center of the circle to any point on its circumference.
Angle (θ): The angle of the sector in degrees.
Sector Area: The area of the portion of the circle bounded by two radii and the arc.

Example Calculation

For a circle with a radius of 10 units and a sector angle of 90 degrees:

\[ \text{Area} = \frac{90}{360} \times \pi \times 10^2 = 78.54 \text{ square units} \]

Frequently Asked Questions (FAQ)

What is a sector?

A sector is a portion of a circle bounded by two radii and their intercepted arc.

How do I find the radius?

The radius is the distance from the center of the circle to its edge. Measure it with a ruler or use a given measurement.

Can I use the calculator for any circle?

Yes, as long as you have the radius and angle, you can find the area of the sector for any circle.

Why is the sector area useful?

Sector area is useful in fields such as architecture, engineering, and any application requiring precise area measurements.

How accurate is this calculator?

This calculator uses precise mathematical formulas to deliver accurate results every time.

Tool developed by Ugo Candido. Content reviewed by Geometry Experts Team.
Last reviewed for accuracy on: October 2023.