1. What is Arch Height?

Arch height (or sagitta) is the distance from the center of the chord to the highest point of the circular arc. It's an important measurement in architecture, engineering, and geometry.

2. How Does the Calculator Work?

The calculator uses the arch height formula:

Where:

• \( r \) — Radius of the circle (feet)
• \( \text{chord} \) — Length of the chord (feet)

Explanation: The formula calculates the maximum height of the arc by subtracting the distance from the circle's center to the chord from the radius.

3. Importance of Arch Height Calculation

Details: Calculating arch height is essential for designing arches, bridges, and curved structures in construction and engineering projects.

4. Using the Calculator

Tips: Enter the radius and chord length in feet. Both values must be positive numbers. The chord length must be less than or equal to twice the radius.

5. Frequently Asked Questions (FAQ)

Q1: What if my chord is longer than twice the radius?
A: This is geometrically impossible for a circular arc. The maximum chord length is equal to the diameter (2 × radius).

Q2: Can I use this for elliptical arches?
A: No, this formula only works for circular arches. Elliptical arches require more complex calculations.

Q3: What units should I use?
A: The calculator uses feet, but you can use any unit as long as both radius and chord are in the same unit.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise for perfect circular arcs. Real-world measurements may have slight variations.

Q5: What's the relationship between arch height and radius?
A: For a given chord length, taller arches have smaller radii, while flatter arches have larger radii.