1. What is Central Angle?

A central angle is an angle whose apex (vertex) is the center of a circle and whose legs (sides) are radii intersecting the circle in two distinct points. It is measured by the arc length divided by the radius of the circle.

2. How Does the Calculator Work?

The calculator uses the central angle formula:

Where:

• \( \theta \) — Central angle in radians
• \( s \) — Arc length (units)
• \( r \) — Radius (units)

Explanation: The central angle is directly proportional to the arc length and inversely proportional to the radius.

3. Importance of Central Angle Calculation

Details: Central angles are fundamental in geometry, trigonometry, and circular motion calculations. They are used in navigation, engineering, and physics to determine angular displacement.

4. Using the Calculator

Tips: Enter arc length and radius in the same units. Both values must be positive numbers. The result is given in radians.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert radians to degrees?
A: Multiply radians by (180/π) to convert to degrees (1 rad ≈ 57.2958°).

Q2: What if I know the angle and need to find arc length?
A: Rearrange the formula: \( s = r \times \theta \).

Q3: Does this work for any circle size?
A: Yes, the formula applies to all circles regardless of size.

Q4: What's the difference between central angle and inscribed angle?
A: Central angle has vertex at the center, while inscribed angle has vertex on the circle.

Q5: Can I use this for partial circles (arcs)?
A: Yes, as long as you know the arc length and radius.