1. What is Chord Length?

A chord of a circle is a straight line segment whose endpoints both lie on the circle. The length of the chord depends on the radius of the circle and the central angle that subtends the chord.

2. How Does the Calculator Work?

The calculator uses the chord length formula:

Where:

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

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

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, and architecture for designing circular structures, calculating segment areas, and solving various geometric problems.

4. Using the Calculator

Tips: Enter the circle's radius and the central angle in degrees. The calculator will automatically convert the angle to radians and compute the chord length.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between chord length and arc length?
A: Chord length is the straight-line distance between two points on a circle, while arc length is the distance along the circumference between those points.

Q2: What's the maximum possible chord length?
A: The maximum chord length is the diameter of the circle (when θ = 180°).

Q3: How does chord length change with angle?
A: Chord length increases as the angle increases from 0° to 180°, then decreases symmetrically from 180° to 360°.

Q4: Can I calculate radius from chord length?
A: Yes, if you know both the chord length and the central angle, you can rearrange the formula to solve for radius.

Q5: What if my angle is in radians?
A: The calculator automatically converts degrees to radians, but if you're working directly with radians, you can use the formula directly.