1. What is Radius?

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is half the length of the diameter and a fundamental measurement in circular geometry.

2. How Does the Calculator Work?

The calculator uses the radius formula:

Where:

• \( r \) — Radius of the circle
• \( C \) — Circumference of the circle
• \( \pi \) — Mathematical constant (~3.14159)

Explanation: The formula derives from the basic circumference formula \( C = 2\pi r \), rearranged to solve for radius.

3. Importance of Radius Calculation

Details: Knowing the radius is essential for calculating other circle properties like area, diameter, and arc length. It's fundamental in engineering, physics, and many practical applications involving circular objects.

4. Using the Calculator

Tips: Enter the circumference in any units (must be greater than 0). The result will be in the same units. For precise results, use exact measurements.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for partial circles (arcs)?
A: No, this calculates the radius of a complete circle. For arcs, you need additional information like arc length and central angle.

Q2: What if I know the diameter instead?
A: Radius is simply half the diameter (\( r = d/2 \)). No calculation needed.

Q3: How precise is the value of pi used?
A: The calculator uses PHP's built-in pi() function which provides sufficient precision for most practical applications.

Q4: Can I calculate circumference from radius?
A: Yes, using the inverse formula \( C = 2\pi r \).

Q5: What units should I use?
A: Any consistent units can be used (cm, inches, meters, etc.). The result will be in the same units as your input.