1. What is the Radius of an Angle?

The radius of an angle refers to the distance from the center of a circle to its circumference, calculated when given the arc length and the central angle in radians. This relationship is fundamental in circular geometry.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

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

Explanation: The formula directly relates the radius to the arc length and the central angle measured in radians.

3. Importance of Radius Calculation

Details: Calculating radius from arc length and angle is essential in various fields including engineering, architecture, physics, and navigation where circular measurements are involved.

4. Using the Calculator

Tips: Enter arc length and angle values in consistent units. Both values must be positive numbers. The angle must be in radians (not degrees).

5. Frequently Asked Questions (FAQ)

Q1: Why must the angle be in radians?
A: The formula r = s/θ is mathematically derived using radians. Using degrees would require a conversion factor (π/180).

Q2: What if I have the angle in degrees?
A: Convert degrees to radians first by multiplying by π/180 (approximately 0.0174533).

Q3: Can this formula be used for any circle?
A: Yes, this formula applies to all circles regardless of size, as long as the angle is measured in radians.

Q4: What are practical applications of this calculation?
A: This calculation is used in designing circular structures, calculating distances in navigation, and solving problems in rotational mechanics.

Q5: How accurate is this calculation?
A: The accuracy depends on the precision of your input values. The calculator provides results with up to 4 decimal places.