1. What is the Circle Circumference Formula?

The circumference (perimeter) of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. This fundamental geometric formula relates the linear distance around a circle to its radius.

2. How Does the Calculator Work?

The calculator uses the circle circumference formula:

Where:

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

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

3. Importance of Circumference Calculation

Details: Calculating circumference is essential in geometry, engineering, construction, and various scientific applications where circular shapes are involved.

4. Using the Calculator

Tips: Enter the radius in any length unit (must be positive). The result will be in the same units as the input.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between circumference and perimeter?
A: Circumference is specifically the perimeter of a circle. Both terms refer to the distance around a shape.

Q2: Can I use diameter instead of radius?
A: Yes, the formula becomes C = πd where d is diameter (d = 2r).

Q3: What are common applications of this calculation?
A: Used in wheel/gear design, circular construction projects, satellite orbits, and any circular motion calculations.

Q4: How accurate is the π value used?
A: The calculator uses PHP's built-in pi() function which is accurate to about 14 decimal places.

Q5: Can this calculate partial circumferences?
A: No, this calculates full circumference. For arc lengths, you'd need the central angle as well.