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. This calculator computes the length of a chord given the radius and central angle.

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 straight-line distance between two points on a circle's circumference that are separated by a given central angle.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, architecture, and various fields where circular measurements are needed, such as designing arches, bridges, and circular structures.

4. Using the Calculator

Tips: Enter the circle's radius and the central angle in radians. Both values must be positive numbers. The result will be in the same units as the radius.

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 chord length possible?
A: The maximum chord length is the diameter (2r), which occurs when θ = π radians (180°).

Q3: How accurate is this calculation?
A: The calculation is mathematically exact, assuming perfect circular geometry and precise inputs.

Q4: Can this be used for other curves besides circles?
A: No, this formula is specific to circular geometry. Other curves require different calculations.

Q5: What if my angle is greater than 2π radians?
A: The formula will still work, but angles > 2π represent more than one full revolution around the circle.