1. What is Arc Length?

Arc length is the distance along the curved line making up the arc. It's calculated using the radius of the circle and the central angle (in radians) that the arc subtends.

2. How Does the Calculator Work?

The calculator uses the arc length formula:

Where:

• \( L \) — Arc length (feet)
• \( r \) — Radius of the circle (feet)
• \( \theta \) — Central angle in radians

Explanation: The arc length is directly proportional to both the radius and the angle (when measured in radians).

3. Importance of Arc Length Calculation

Details: Arc length calculations are essential in geometry, engineering, architecture, and physics for designing curved structures and analyzing circular motion.

4. Using the Calculator

Tips: Enter radius in feet and angle in radians. Both values must be positive numbers. Remember that 180° equals π radians (about 3.1416 radians).

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: The formula requires radians. Convert degrees to radians by multiplying by π/180.

Q2: What if my angle is more than 2π radians?
A: The formula works for any positive angle, but angles >2π represent more than one full rotation.

Q3: Does this work for partial circles?
A: Yes, the formula works for any arc, whether it's part of a circle or multiple full rotations.

Q4: What are practical applications of arc length?
A: Used in designing roads, roller coasters, arches, calculating satellite orbits, and more.

Q5: How precise should my measurements be?
A: For most practical purposes, 2-3 decimal places are sufficient, but precision depends on your specific application.