Central Angle Calculator

How to Use the Central Angle Calculator

1. Enter the radius of the circle in the "Radius" field. This is the distance from the center of the circle to any point on the circle's edge.
2. Enter the arc length in the "Arc Length" field. This is the distance along the curved edge of the circle between two points.
3. Click the "Calculate" button to compute the central angle.
4. The result will be displayed in both degrees and radians.

Understanding the Formula

The central angle θ can be calculated using the formula:

θ = (s/r) × (180/π)

Where:

• s = Arc Length
• r = Radius
• π = Pi (approximately 3.14159)
• θ = Central Angle in degrees

Example

If a circle has a radius of 10 units and an arc length of 20 units, the central angle would be:

θ = (20/10) × (180/π) ≈ 114.59°

Applications

This calculator can be used in various fields including:

• Geometry and trigonometry problems
• Engineering and architecture for designing circular structures
• Navigation and astronomy calculations
• Computer graphics and animation