What is the formula for the circumference of a circle?

The formula for the circumference of a circle is \( C = 2\pi r \) or \( C = \pi d \).

The circumference of a circle is the distance around the edge of the circle. To calculate this, you can use either the radius (r) or the diameter (d) of the circle. The radius is the distance from the centre of the circle to any point on its edge, while the diameter is the distance across the circle, passing through the centre, and is twice the length of the radius.

The formula \( C = 2\pi r \) uses the radius. Here, \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159. So, if you know the radius of the circle, you simply multiply it by 2 and then by \( \pi \) to find the circumference.

Alternatively, the formula \( C = \pi d \) uses the diameter. Since the diameter is twice the radius, this formula is essentially the same as the first one but skips the step of doubling the radius. You just multiply the diameter by \( \pi \) to get the circumference.

These formulas are fundamental in geometry and are very useful in various real-life applications, such as finding the length of a circular track or the perimeter of a round table. Understanding and using these formulas will help you solve many problems involving circles in your GCSE Maths exams.