1. What is a Circle Segment?

A segment of a circle is the region bounded by a chord and the arc subtended by that chord. It's essentially the area of a "slice" of the circle minus the triangular portion.

2. How Does the Calculator Work?

The calculator uses the segment area formula:

Where:

• \( A \) — Area of the segment
• \( r \) — Radius of the circle
• \( \theta \) — Central angle in radians

Explanation: The formula calculates the area of the sector and subtracts the area of the triangular portion to get just the segment area.

3. Importance of Segment Calculation

Details: Segment area calculations are important in geometry, engineering, and architecture for designing circular components, arches, and analyzing cross-sections.

4. Using the Calculator

Tips: Enter the radius and central angle in radians. Remember to convert degrees to radians if needed (1° = π/180 radians).

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 180° = π radians.

Q2: What's the difference between a sector and a segment?
A: A sector includes the triangular portion, while a segment excludes it.

Q3: Can I use this for partial circles?
A: Yes, as long as you know the radius and central angle.

Q4: What if my angle is greater than 2π?
A: The calculator will still work, but angles > 2π represent more than one full rotation.

Q5: How precise are the results?
A: Results are precise to 4 decimal places, but actual precision depends on input accuracy.