Which formula gives the circumference of a circle?

The circumference is 2 times pi times the radius, equivalently pi times the diameter, since the diameter is twice the radius. Pi is defined as exactly that ratio, the distance around a circle divided by the distance across it, and the remarkable thing is that this ratio is the same for every circle no matter its size, which is what makes it a constant worth naming. Its value is a little over 3.14, and it is irrational, meaning its decimal expansion never ends or repeats. Confusion with the area formula is the classic error, and the units offer a check: circumference is a length, so it must involve the radius to the first power, while area is a square measure and must involve the radius squared. If you ever forget which is which, remember that pi r squared has the squared term and therefore has to be the area. The same logic extends to spheres, whose surface area and volume also scale by different powers.

Because pi is irrational, no circle can have both a whole number diameter and a whole number circumference.