1. What is Arc Length?

Arc length is the distance along the curved line of a circle or other curved shape. It represents the portion of the circumference between two points on a circle, measured in linear units.

2. How Does the Calculator Work?

The calculator uses the arc length formula:

Where:

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

Explanation: The formula calculates the length of an arc by multiplying the radius of the circle by the angle (in radians) that the arc subtends at the center of the circle.

3. Importance of Arc Length Calculation

Details: Calculating arc length is essential in geometry, engineering, architecture, and physics. It helps determine distances along curved paths, design circular structures, and solve problems involving circular motion.

4. Using the Calculator

Tips: Enter the radius in any consistent units and the angle in radians. Both values must be positive numbers. The result will be in the same units as the radius.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees instead of radians?
A: Convert degrees to radians first by multiplying by π/180. For example, 180° = π radians.

Q2: Can I use this formula for any circle?
A: Yes, this formula works for any circle regardless of size, as long as you have the radius and angle in radians.

Q3: What's the difference between arc length and chord length?
A: Arc length is the distance along the curved line, while chord length is the straight-line distance between the two endpoints of the arc.

Q4: Does this formula work for partial circles?
A: Yes, the formula works for any arc of a circle, whether it's a small segment or a full circle (when θ = 2π).

Q5: What are some practical applications of arc length?
A: Arc length calculations are used in designing roads, calculating material needed for curved structures, determining distances in navigation, and in various physics calculations involving circular motion.