1. What is Chord Length?

A chord is a straight line connecting two points on a curve, typically a circle. The chord length is the distance between these two points.

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 circle's radius and the angle between the two radii connecting to the chord's endpoints.

3. Applications of Chord Length

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

4. Using the Calculator

Tips: Enter the radius and central angle in radians. Both values must be positive numbers. For degrees, convert to radians first (radians = degrees × π/180).

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 curved part of the circle between those points.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533). Many calculators have a degree-to-radian conversion function.

Q3: What's the maximum possible chord length?
A: The maximum chord length is the diameter of the circle (2 × radius), which occurs when the central angle is π radians (180 degrees).

Q4: Can this be used for other curves besides circles?
A: This specific formula only applies to perfect circles. Other curves require different calculations.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circles, assuming precise input values.