1. What is a Chord Length?

A chord of a circle is a straight line segment whose endpoints both lie on the circle. The chord length is the distance between these two endpoints.

2. How Does the Calculator Work?

The calculator uses the chord length formula:

Where:

• \( c \) — Chord length (same units as radius)
• \( r \) — Radius of the circle
• \( \theta \) — Central angle in radians

Explanation: The formula calculates the length of the chord based on the radius and the central angle that subtends the chord.

3. Importance of Chord Calculation

Details: Chord length calculations are essential in geometry, engineering, and architecture for designing circular structures and analyzing circular motion.

4. Using the Calculator

Tips: Enter the radius and central 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. Convert degrees to radians by multiplying 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 is this different from arc length?
A: Chord length is the straight-line distance between points, while arc length is the distance along the curve of the circle between those points.

Q4: What if I know the chord length and want to find the angle?
A: You can rearrange the formula: θ = 2 × arcsin(c/(2r))

Q5: Does this work for any circle size?
A: Yes, the formula works for any circle as long as you have valid radius and angle values.