1. What is Chord Length?

A chord is a straight line segment whose endpoints lie on a circular arc. In geometry, the chord length represents the distance between two points on a circle's circumference.

2. How Does the Calculator Work?

The calculator uses the chord length formula:

Where:

• \( r \) — Radius of the circle
• \( h \) — Sagitta height (distance from chord to arc)

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

3. Applications of Chord Length Calculation

Details: Chord length calculations are essential in various fields including architecture, engineering, surveying, and manufacturing. They're used in designing arches, calculating material requirements, and determining clearances in circular structures.

4. Using the Calculator

Tips: Enter the radius and sagitta height in consistent units (meters or feet). Both values must be positive numbers, and the sagitta height must be less than the radius for a valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is sagitta height?
A: Sagitta (or versine) is the height from the chord to the arc of a circle, representing the maximum distance between the chord and the arc.

Q2: Can I calculate chord length with different inputs?
A: Yes, chord length can also be calculated using the central angle and radius with the formula: Chord Length = 2r × sin(θ/2).

Q3: What if my sagitta height equals the radius?
A: When h = r, the chord length becomes zero, which represents a degenerate case where the chord reduces to a single point.

Q4: Are there limitations to this formula?
A: The formula assumes a perfect circle and works for all cases where the sagitta height is less than or equal to the radius.

Q5: Can this calculator handle different units?
A: The calculator works with any consistent unit system (meters, feet, inches, etc.) as long as both inputs use the same unit.