1. What is the Arch Radius Formula?

The arch radius formula calculates the radius of a circular arch given its chord length and height. This is essential in architecture and engineering for designing arches and curved structures.

2. How Does the Calculator Work?

The calculator uses the arch radius formula:

Where:

• \( r \) — Radius of the arch (feet)
• \( chord \) — Length of the chord (feet)
• \( height \) — Height of the arch (feet)

Explanation: The formula combines the geometric relationships between a circle's chord, height, and radius to determine the radius of the circle that would form the arch.

3. Importance of Arch Radius Calculation

Details: Calculating arch radius is crucial for architectural design, bridge construction, and any project involving curved structures. It helps determine the proper curvature needed for structural integrity and aesthetic appeal.

4. Using the Calculator

Tips: Enter chord length and height in feet. Both values must be positive numbers. The calculator will compute the radius of the circular arch that would pass through these points.

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 the arch's endpoints, while arc length is the distance along the curved arch itself.

Q2: Can this formula be used for any arch shape?
A: This formula specifically calculates the radius for a circular arch. Other arch shapes (parabolic, elliptical) require different formulas.

Q3: What if my arch height is very small compared to the chord?
A: The formula works for all valid height values, but very flat arches will have very large radii.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise for perfect circular arches. Real-world applications should account for material properties and construction tolerances.

Q5: Can I use different units besides feet?
A: Yes, as long as both chord and height are in the same units, the radius will be in those same units.