1. What is Arc Length?

Arc length is the distance along the curved line that makes up the arc of a circle. It is calculated using the formula L = r × θ, where r is the radius of the circle and θ is the central angle in radians.

2. How Does the Calculator Work?

The calculator uses the arc length formula:

Where:

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

Explanation: The formula calculates the distance along the circumference of a circle between two points determined by the central angle.

3. Importance of Arc Length Calculation

Details: Arc length calculations are essential in geometry, engineering, architecture, and physics for designing curved structures, calculating distances along circular paths, and solving problems involving circular motion.

4. Using the Calculator

Tips: Enter the radius in meters and the angle in radians. Both values must be positive numbers. The calculator will compute the arc length in meters.

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: The formula requires radians. To convert degrees to radians, multiply by π/180.

Q2: What if my angle is greater than 2π radians?
A: The formula works for any positive angle value, but angles greater than 2π represent more than one full revolution around the circle.

Q3: Does this work for partial circles?
A: Yes, the formula calculates the length of any circular arc, whether it's a full circle or a partial segment.

Q4: What are practical applications of arc length?
A: Applications include designing curved roads, calculating material needed for arched structures, and determining distances in circular motion problems.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circles. The accuracy depends on the precision of your radius and angle measurements.