1. What is a Chord Length?

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

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 separated by a given central angle.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, architecture, and various applications involving circular shapes and measurements.

4. Using the Calculator

Tips: Enter the radius and angle values. Both must be positive numbers. The angle should be in radians (to convert from degrees, multiply by 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 path between those points.

Q2: Can I use degrees instead of radians?
A: The formula requires radians. Convert degrees to radians by multiplying by π/180 (approximately 0.0174533).

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

Q4: How is chord length related to sagitta?
A: Sagitta is the height of the arc. Chord length, sagitta, and radius are related by the formula: sagitta = r - √(r² - (chord/2)²).

Q5: What are practical applications of chord length?
A: Used in construction (arches, circular structures), manufacturing (circular parts), navigation (great circle routes), and computer graphics.