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 defined by a central angle.

2. How Does the Calculator Work?

The calculator uses the arc length formula:

Where:

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

Explanation: The length of an arc is directly proportional to both the radius of the circle and the central angle that subtends it.

3. Importance of Arc Length Calculation

Details: Calculating arc length is essential in geometry, engineering, architecture, and physics for designing curved structures, analyzing circular motion, and solving various practical problems involving circular segments.

4. Using the Calculator

Tips: Enter the radius in any length units (must be > 0) and the angle in radians (must be > 0). The result will be in the same units as the radius.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees?
A: Convert degrees to radians first (radians = degrees × π/180). Most calculators have a degree-to-radian conversion function.

Q2: Can I use negative values for radius or angle?
A: No, both radius and angle must be positive values in this calculation.

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

Q4: How does arc length relate to sector area?
A: Sector area = (1/2) × radius × arc length = (1/2) × r² × θ.

Q5: What's the maximum possible arc length?
A: For a given radius, the maximum arc length is the circumference (2πr), which occurs when θ = 2π radians (360 degrees).