1. What is Arc Length?

Arc length is the distance along the curved line of a circle's circumference. It's calculated using the radius of the circle and the central angle (in radians) 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 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, physics, and many practical applications like designing curved structures, calculating distances in circular motion, and computer graphics.

4. Using the Calculator

Tips: Enter the radius of your circle and the angle in radians. Remember that 180 degrees equals π radians (about 3.14159 radians). All values must be positive numbers.

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, representing multiple full rotations around the circle.

Q3: Does this work for partial circles?
A: Yes, the formula calculates the length for any portion of the circumference determined by the angle.

Q4: What units does this use?
A: The arc length will be in whatever units you use for the radius. The angle must always be in radians.

Q5: Can I calculate radius from arc length and angle?
A: Yes, by rearranging the formula: \( r = \text{Arc Length} / \theta \).