1. What is the Radius Formula?

The radius formula calculates the radius of a circle from the arc length and central angle. It is derived from the fundamental relationship between arc length, radius, and angle in circular geometry.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

• \( r \) — Radius of the circle (m)
• \( L \) — Arc length (m)
• \( \theta \) — Central angle (radians)

Explanation: The formula directly relates the radius to the arc length and central angle, where the arc length is proportional to both the radius and the angle.

3. Importance of Radius Calculation

Details: Calculating radius from arc length is essential in geometry, engineering, architecture, and various technical fields where circular measurements are involved.

4. Using the Calculator

Tips: Enter arc length in meters and angle in radians. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why must the angle be in radians?
A: The formula r = L/θ requires the angle to be in radians because the radian is the natural unit for angular measurement in circular geometry.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 to convert to radians (radians = degrees × π/180).

Q3: What if I have the angle in degrees?
A: Convert the angle to radians first before using this calculator, or use a calculator that accepts degrees as input.

Q4: Can this formula be used for any circle?
A: Yes, this formula applies to all circles regardless of size, as long as the arc length and central angle are known.

Q5: What are typical applications of this calculation?
A: This calculation is used in construction, mechanical engineering, navigation, and any field involving circular motion or curved structures.