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 that subtends the arc.

2. How Does the Calculator Work?

The calculator uses the arc length formula:

Where:

• \( r \) — Radius of the circle
• \( \theta \) — Central angle in radians

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

3. Importance of Arc Length Calculation

Details: Calculating arc length is essential in geometry, engineering, and physics for determining distances along curved paths, designing circular structures, and analyzing rotational motion.

4. Using the Calculator

Tips: Enter the radius and angle in radians. Both values must be positive numbers. Remember that 180° equals π 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 greater than 2π?
A: The formula works for any positive angle, but angles >2π represent multiple full rotations.

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

Q4: What are practical applications of this calculation?
A: Used in designing roads, roller coasters, gears, and any application involving circular motion or curved surfaces.

Q5: How accurate is this calculation?
A: The formula is mathematically exact for perfect circular arcs. Accuracy depends on your input measurements.