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 a chord can be calculated using 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:

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

Explanation: The formula calculates the length of a chord based on the radius and the angle that subtends the chord at the center of the circle.

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 involving circles.

4. Using the Calculator

Tips: Enter the radius of the circle and the central angle in radians. Both values must be positive numbers. The calculator will compute the chord length in the same units as the radius.

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: The formula requires the angle in 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 is this different from 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.

Q4: What if I know the chord length and need 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 circles of any size as long as the angle is in radians and the radius is positive.