1. What is Circumference?

The circumference of a circle is the linear distance around its edge. It's the circle's perimeter and is directly related to its radius through the mathematical constant π (pi).

2. How Does the Calculator Work?

The calculator uses the circumference formula:

Where:

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

Explanation: The formula shows that circumference is proportional to the radius, with 2π being the constant of proportionality.

3. Importance of Circumference Calculation

Details: Calculating circumference is fundamental in geometry, engineering, and physics. It's used in designing circular objects, calculating rotational motion, and solving real-world problems involving circular shapes.

4. Using the Calculator

Tips: Enter the radius in any length unit (meters, inches, etc.). The result will be in the same units. The radius must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radius and diameter?
A: The radius is half the diameter. The formula can also be written as \( C = \pi d \) where d is diameter.

Q2: How precise is the value of π used?
A: The calculator uses PHP's built-in pi() function which provides sufficient precision for most practical applications.

Q3: Can I calculate radius from circumference?
A: Yes, the formula can be rearranged as \( r = C / (2\pi) \).

Q4: Why is π involved in the formula?
A: π is the fundamental constant relating a circle's circumference to its diameter in Euclidean geometry.

Q5: What are some real-world applications?
A: Calculating fencing needed for circular areas, determining wheel rotations, designing pipes, and many engineering applications.