The relationship between a circle's circumference \( C \) and its diameter \( d \) is expressed by the formula:
\[ C = \pi d \]
Here, \( \pi \) (pi) is a constant approximately equal to 3.14159. Alternatively, if you want to express it in terms of the radius \( r \) of the circle, the formula can also be written as:
\[ C = 2\pi r \]
Where \( r \) is half of the diameter (\( d = 2r \)).