What is the formula used to calculate the circumference of a circle?

The formula used to calculate the circumference of a circle is based on the relationship between the circle's radius and its diameter. The correct formula, represented in one of the choices, is 2πR, where R stands for the radius of the circle. This formula is derived from the definition of the circumference as the distance around the circle.

Circumference can also be calculated using the diameter (D) of the circle since the diameter is twice the radius (D = 2R). Therefore, substituting D into the circumferential formula yields C = πD, which is another valid expression for the circumference but does not directly utilize the radius.

Other choices provided don't represent the circumference accurately. πR² is actually the formula for the area of a circle, not its circumference. R/2 also doesn't relate to the circumference, as it simply represents half of the radius without bearing any necessary relation to the perimeter of the circle. The 2πR formula appropriately reflects the total distance around the circle, making it clear that both the radius and the constant π factor into this essential geometric measurement.