Circumference of Circles

The circumference is the perimeter of a circle — the distance all the way around its edge. For any circle, the ratio of circumference to diameter is always the same special number: $\pi$ (pi) $\approx 3.14159\ldots$ So if you know the diameter $d$ or the radius $r$, you can find the circumference with one formula.

$\pi$ is the ratio of any circle's circumference to its diameter: $\pi = C \div d$. Measure any circular object — a plate, a coin, a wheel — divide its circumference by its diameter, and you always get approximately $3.14159\ldots$ This works for every circle, no matter how big or small. $\pi$ is irrational: it cannot be written as a simple fraction (though $\frac{22}{7}$ is a useful approximation).

If the problem gives you the diameter, plug straight into $C = \pi d$. No need to halve first. This is the most direct route when $d$ is known.

Example: $d = 15$ m $\Rightarrow C = \pi \times 15 \approx 47.12$ m.

To leave the answer in exact form, write $C = 15\pi$ m.

If the problem gives the radius, multiply by $2\pi$. Do not forget the factor of 2 — this is the most common careless error. The $2$ comes from the fact that the diameter equals two radii: $d = 2r$.

Example: $r = 7$ cm $\Rightarrow C = 2\pi \times 7 = 14\pi \approx 43.98$ cm.

Rearrange the circumference formula to find diameter or radius:

From $C = \pi d$:   $d = \dfrac{C}{\pi}$

From $C = 2\pi r$:   $r = \dfrac{C}{2\pi}$

Example: $C = 44$ cm. Using $\pi \approx \frac{22}{7}$: $r = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7$ cm exactly.