1. What is Radius Calculation From Chord Height?

This calculator determines the radius of a circle when given the chord length and sagitta (the height from the chord to the arc). This is a fundamental geometric calculation used in various engineering and construction applications.

2. How Does the Calculator Work?

The calculator uses the geometric formula:

Where:

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

Explanation: This formula derives from the geometric relationship between a chord, its sagitta, and the circle's radius, using the Pythagorean theorem in circular segments.

3. Applications of Radius Calculation

Details: This calculation is essential in architecture, bridge design, pipe fabrication, and any application involving circular arcs where only chord and height measurements are available.

4. Using the Calculator

Tips: Enter chord length and sagitta in consistent units (meters or feet). Both values must be positive numbers greater than zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is sagitta in circular geometry?
A: Sagitta is the perpendicular distance from the midpoint of a chord to the arc of the circle.

Q2: Can this formula be used for any circle segment?
A: Yes, this formula works for any circular segment where you know the chord length and sagitta height.

Q3: What units should I use for measurements?
A: Use consistent units (meters, feet, inches, etc.) for both chord and sagitta. The result will be in the same units.

Q4: Is there a minimum sagitta value required?
A: The sagitta must be greater than zero and less than the radius. Extremely small sagitta values relative to chord length may affect calculation precision.

Q5: Can this calculation be used for elliptical arcs?
A: No, this formula is specific to circular arcs. Elliptical arcs require different geometric relationships.