Circular Segment Area Calculator

Data Source and Methodology

All calculations are based on standard mathematical formulas. For more information, visit the Wikipedia page on Circular Segments. All calculations are rigorously based on these formulas and data.

The Formula Explained

The area of a circular segment can be calculated using the formula:

Glossary of Terms

• Radius (r): The distance from the center of the circle to the edge.
• Central Angle (θ): The angle subtended by the segment at the center of the circle, measured in radians.
• Area: The size of the segment in square units.

How It Works: A Step-by-Step Example

Suppose you have a circle with a radius of 5 units and a central angle of 1 radian. Using the formula, the area of the segment is calculated as:

\[ \text{Area} = \frac{5^2}{2} (1 - \sin(1)) \]

Frequently Asked Questions (FAQ)

What is a circular segment?

A circular segment is the region of a circle cut off by a chord.

How do you calculate the area of a circular segment?

The area can be calculated using the formula: Area = r²/2 * (θ - sin(θ)), where r is the radius and θ is the central angle in radians.

What is the difference between a segment and a sector?

A sector is the region of a circle bounded by two radii and an arc, while a segment is the region bounded by a chord and an arc.

What units should the radius and angle be in?

The radius should be in consistent units (e.g., meters, centimeters), and the angle should be in radians.

Why is the angle in radians?

Radians are a standard unit in mathematics for measuring angles, especially when dealing with trigonometric functions.