1. What is an Arc Length Calculator?

Definition: This calculator computes the length of a circular arc based on the radius of the circle and the central angle in radians.

Purpose: It helps in geometry, engineering, and physics calculations where circular segments are involved.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The arc length is simply the product of the radius and the angle (in radians) that the arc subtends at the center.

3. Importance of Arc Length Calculation

Details: Accurate arc length calculations are essential in designing curved structures, calculating distances along circular paths, and in various trigonometric applications.

4. Using the Calculator

Tips: Enter the radius in meters and the angle in radians. Remember that π radians = 180°. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 180° = π radians, 90° = π/2 radians.

Q2: What if I only have the chord length?
A: You'll need additional information. With chord length (c) and radius (r), you can find θ using θ = 2 arcsin(c/(2r)).

Q3: Does this work for partial circles?
A: Yes, the formula works for any angle θ ≤ 2π (360°). For θ = 2π, you get the full circumference (2πr).

Q4: Can I use different units?
A: Yes, but ensure consistent units. If radius is in feet, arc length will be in feet.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circular arcs.