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

The formula for calculating the circumference of a circle is correctly represented by both πd and 2πr. Here’s why these formulas are valid.

Circumference is the distance around the edge of a circle. The relationship between the diameter (d) of the circle and its radius (r) is essential here: the diameter is twice the radius, which means d = 2r.

When using the diameter in the formula, you get the circumference as π times the diameter: C = πd. This is a direct correlation and is commonly used when the diameter is known or provided in a problem.

Alternatively, when using the radius, since the diameter is twice the radius, substituting gives the same circumference, represented as C = 2πr. Both formulas will yield the same numerical answer, thus affirming their validity.

However, the area of a circle (A = πr²) and the formula for a measure that might suggest a linear addition like 2d (which simply represents double the diameter) do not pertain to circumference directly.

Thus, the fundamental understanding of circumference being either expressed through diameter or radius allows you to utilize either formula accurately depending on the information given in a problem.