Circle: circumference & area

How far does your bike travel in one turn of the wheel? And is the large pizza really worth it, or are two small ones enough? Both questions literally revolve around the circle. With two formulas and one famous number you can calculate the answers instead of guessing.

Radius, diameter and the number π

The radius r is the distance from the centre to the edge. The diameter d goes all the way across the circle, straight through the centre, so d = 2 · r. And now the amazing part: for every circle, whether coin or Ferris wheel, the circumference is about 3.14 times as long as the diameter. This fixed ratio of circumference to diameter is called π (pi). Strictly speaking π has infinitely many decimal places (3.14159…), for our calculations π ≈ 3.14 is enough.

The circumference: C = 2 · π · r

Because the circumference is π times the diameter, C = π · d, and with d = 2 · r this becomes C = 2 · π · r. An example: a circle with radius 5 cm has circumference C = 2 · 3.14 · 5 = 31.4 cm. The circumference is a length, so you measure it in cm or m.

The area: A = π · r²

For the area, A = π · r². The radius is squared first, then multiplied by π. So the same circle with radius 5 cm has area A = 3.14 · 25 = 78.5 cm². Because two lengths come together here, the result is an area, measured in cm² or m². Note the difference: the radius enters the circumference directly, but the area as a square. Doubling the radius therefore gives four times the area. For the same reason the large pizza wins: at 20 cm diameter the radius is 10 cm, which gives 3.14 · 10² = 314 cm² per pizza, so 628 cm² for two. At 30 cm diameter the radius is 15 cm, which gives 3.14 · 15² = 706.5 cm² in one go.