Circumference of a circle

What the symbols mean

$C$

the circumference: the perimeter of the circle

$r$

the radius

$\pi$

pi, about 3.14159

When to use it

Use it for the distance round anything circular: how far a wheel rolls in one turn, the length of a running track's bend, the amount of fencing round a round pond. Working backwards, measure round a tree trunk with a tape and divide by $2\pi$ to get its radius.

Why it works

This is the definition of π: every circle's circumference divided by its diameter gives the same number, and we call it π. Since the diameter is $2r$, the circumference is $\pi \times 2r$.

Common mistakes

• Mixing up $2\pi r$ (circumference) and $\pi r^2$ (area). Check units: a length cannot come out in cm².
• Using the diameter in $2\pi r$, which doubles the answer.
• Forgetting that a rolling wheel's distance per turn is its circumference, not its diameter.