1. What is Chord Length?

A chord is a straight line segment whose endpoints lie on a circular arc. 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
• \( \theta \) — Arc angle in radians

Explanation: The formula calculates the straight-line distance between two points on a circle separated by a given arc angle.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, architecture, and various technical fields where circular measurements are involved.

4. Using the Calculator

Tips: Enter the radius and arc angle in radians. Both values must be positive numbers. The result will be in the same units as the radius input.

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 the angle in radians. To convert from degrees to radians, multiply by π/180.

Q3: What if I know the chord length and want to find the angle?
A: You can rearrange the formula: θ = 2 × arcsin(chord/(2r)).

Q4: Does this work for any circle size?
A: Yes, the formula works for circles of any size, as long as the angle is less than or equal to π radians (180 degrees).

Q5: What are practical applications of chord length calculations?
A: Used in construction, manufacturing, navigation, computer graphics, and any field dealing with circular geometry.