What is the formula for the circumference of a circle?

The formula for the circumference of a circle is indeed represented as (C = 2\pi r), where (C) represents the circumference and (r) is the radius of the circle. This formula emerges from the relationship between the diameter and the radius, as the diameter of a circle is twice the radius (i.e., (d = 2r)). Since the circumference is the distance around the circle, it can also be expressed in terms of the diameter: (C = \pi d). By substituting (d) with (2r), we arrive at the formula (C = 2\pi r).

This equation illustrates that the circumference is directly proportional to the radius, meaning that as the radius increases, the circumference also increases in a linear manner, multiplied by the constant (\pi). Understanding this formula is fundamental in geometry and is frequently used in various applications, including physics, engineering, and everyday calculations involving circular objects.