1. What is Arc Length?

Arc length is the distance along the curved line making up the arc. It's a portion of the circumference of a circle determined by the central angle θ and the radius r.

2. How Does the Calculator Work?

The calculator uses the arc length formula:

Where:

• \( \theta \) — Central angle in radians
• \( r \) — Radius of the circle
• arc — Length of the arc (same units as radius)

Explanation: The formula calculates how much of the circle's circumference is covered by the given angle. Since full circumference is \( 2\pi r \), an angle of θ radians covers \( \theta/(2\pi) \) of the circumference.

3. Importance of Arc Length Calculation

Details: Arc length is fundamental in geometry, engineering, and physics. It's used in designing curved structures, calculating distances along circular paths, and in trigonometric applications.

4. Using the Calculator

Tips: Enter angle in radians (convert from degrees by multiplying by π/180), and radius in any length unit. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533). Example: 180° = π radians.

Q2: Can I use this for any circular arc?
A: Yes, as long as you have the central angle in radians and the radius.

Q3: What if my angle is in degrees?
A: First convert to radians: θ (radians) = θ (degrees) × π/180.

Q4: Does the radius unit matter?
A: The arc length will be in whatever units you use for radius (cm, m, inches, etc.).

Q5: What's the relationship between arc length and circumference?
A: Circumference is the arc length for a full circle (θ = 2π radians).