1. What is Chord Length?

A chord is a straight line connecting two points on a curve, typically a circle. The length of a chord can be calculated when you know the radius of the circle and the angle (in radians) subtended by the chord at the center.

2. How Does the Calculator Work?

The calculator uses the chord length formula:

Where:

• \( c \) — Chord length
• \( r \) — Radius of the circle
• \( \theta \) — Angle subtended by the chord (in radians)

Explanation: The formula calculates the length of the chord based on trigonometric relationships in a circle.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, architecture, and various fields where circular measurements are needed.

4. Using the Calculator

Tips: Enter the radius of the circle and the angle in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: The formula requires radians. To convert degrees to radians, multiply by π/180.

Q2: What's the maximum chord length possible?
A: The maximum chord length is the diameter of the circle (2r), which occurs when θ = π radians (180 degrees).

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect circle.

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

Q5: Can this be used for other curves besides circles?
A: No, this formula is specific to circular arcs. Other curves have different chord length formulas.