The circumference of the circle

The circle and its measurements

A circle is defined by its centre and its radius r (the distance from the centre to any point on the circle). The diameter d is twice the radius: d = 2 × r. The outline of the circle is called the circumference, which is precisely the perimeter of the circle.

The formula for the perimeter

P = 2 × π × r

or, using the diameter:

P = π × d

The number π (pi) is a mathematical constant with an approximate value of π ≈ 3.14. Your calculator usually has a π key which gives more decimal places.

Example

For a circle with a radius r = 5 cm: P = 2 × 3.14 × 5 = 31.4 cm

For a circle with a diameter d = 10 cm (so r = 5 cm), we get the same result: P = 3.14 × 10 = 31.4 cm

Common pitfalls

1. Confusing radius and diameter: always check which measurement you are using before choosing the formula.
2. Forgetting the factor 2 when using the radius (P = 2 × π × r, not π × r).
3. Rounding π too early in a multi-step calculation, which leads to accumulated errors: keep π or 3.14 until the final result.