1. What is the Arch Length Formula?

The arch length formula calculates the distance along the curved line making up the arc. It's a fundamental calculation in geometry and engineering for circular segments.

2. How Does the Calculator Work?

The calculator uses the arch length formula:

Where:

• \( \pi \) — Mathematical constant (~3.14159)
• \( r \) — Radius of the circle (feet)
• \( \theta \) — Central angle subtended by the arc (degrees)

Explanation: The formula converts the angle from degrees to radians (by dividing by 180) and multiplies by the radius to get the arc length.

3. Practical Applications

Details: Arch length calculations are essential in architecture, engineering, construction, and any field dealing with circular measurements. They're used in designing bridges, arches, circular tracks, and more.

4. Using the Calculator

Tips: Enter the radius in feet and the angle in degrees. Both values must be positive numbers (radius > 0, angle between 0-360).

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in radians?
A: For radians, use the simpler formula: Length = r × θ (where θ is in radians).

Q2: Does this work for partial circles?
A: Yes, the formula works for any arc length, whether it's a full circle (360°) or a partial segment.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise for perfect circular arcs. Real-world measurements may vary slightly due to material properties.

Q4: Can I use different units?
A: Yes, as long as you're consistent. If you input radius in meters, the length will be in meters.

Q5: What's the relationship between chord length and arc length?
A: Chord length is the straight-line distance between the arc's endpoints, while arc length follows the curve. They're equal only at 0°.