1. What is Chord Length (Arc Width)?

The chord length (or arc width) is the straight-line distance between two points on a curve. In circular geometry, it's the length of the line segment whose endpoints lie on the circle.

2. How Does the Calculator Work?

The calculator uses the chord length formula:

Where:

• \( r \) — Radius of the circle (length units)
• \( \theta \) — Central angle in radians

Explanation: The formula calculates the straight-line distance between two points on a circle given the radius and the angle between them.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, architecture, and various design applications where circular segments are involved.

4. Using the Calculator

Tips: Enter the radius in any consistent length units 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 possible chord length?
A: The maximum chord length is the diameter of the circle (2r), which occurs when θ = π radians (180 degrees).

Q3: How does chord length relate to arc length?
A: Arc length is the distance along the curve (rθ), while chord length is the straight-line distance between the endpoints.

Q4: What if my angle is greater than 2π radians?
A: The calculator will still work, but angles > 2π (360°) represent more than one full rotation around the circle.

Q5: Can this be used for partial circles (arcs)?
A: Yes, the formula works for any circular arc, whether it's a minor arc (θ < π) or major arc (θ > π).