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 determines the length of a chord given the circle's radius and the height of the segment (perpendicular distance from chord to circle).

2. How Does the Calculator Work?

The calculator uses the chord length formula:

Where:

• \( c \) — Chord length
• \( r \) — Radius of the circle
• \( h \) — Height of the segment (perpendicular distance from chord to circle)

Explanation: The formula is derived from the Pythagorean theorem applied to the right triangle formed by the radius, half the chord, and the radius minus the height.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, architecture, and various design applications where circular segments are involved.

4. Using the Calculator

Tips: Enter the radius and height in consistent units. The height must be less than or equal to twice the radius (h ≤ 2r) for a valid solution.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between chord length and arc length?
A: While chord length is the straight-line distance, arc length is the distance along the curve. They're related through the central angle.

Q2: Can I calculate the radius if I know chord length and height?
A: Yes, the formula can be rearranged: \( r = \frac{h}{2} + \frac{c^2}{8h} \)

Q3: What's the maximum possible chord length?
A: The maximum chord length is the diameter (when h = r), which equals 2r.

Q4: How is this different from sagitta length?
A: Sagitta is another term for the height (h) in this calculation - the perpendicular distance from chord to circle.

Q5: What applications use chord length calculations?
A: Common in bridge design, arch construction, circular saw blade design, and any application involving circular segments.