What is the formula for calculating the circumference of a circle?

The formula for calculating the circumference of a circle is derived from the relationship between a circle's diameter, radius, and the mathematical constant π (pi). The circumference represents the total distance around the circle.

The formula 2πr is based on the radius (r) of the circle, where π is approximately equal to 3.14159. In this formula, multiplying the radius by 2 gives the diameter of the circle, and then multiplying by π provides the circumference. This reflects the fundamental property of circles that relates their dimensions to this constant.

Additionally, the circumference can also be expressed using the diameter (d) of the circle through the formula πd, which is equivalent to 2πr since the diameter is twice the radius (d = 2r). However, using 2πr with the radius can sometimes make calculations easier, especially when the radius is given directly.

The other options provided do not relate to the circumference of a circle. The length times width option does not apply since it generally refers to the area of a rectangle rather than a circle. The option of r² is related to the area of a circle, not its circumference. Thus, the most direct and widely used formula for determining the circumference is indeed