Math101 · Independent Ontario learning library
Math101Circumference
Circumference is the distance around a circle. It equals $C=2\pi r$ or $C=\pi d$, where $d=2r$.
Circumference measures borders, wheel travel, belts, pipes, and circular tracks. Its direct proportionality to diameter defines $\pi$.
Intuition and core definition
Circumference is the distance around a circle. It equals $C=2\pi r$ or $C=\pi d$, where $d=2r$. The constant $\pi$ is the ratio of circumference to diameter for every circle, so it measures a universal scaling relationship.
Notation, language, and conditions
$C$ has linear units. An exact value retains $\pi$; an approximation uses $\approx$ and a stated rounding level. Circumference differs from disk area $\pi r^2$ and from an arc length, which is only a fraction of the full boundary.
Why this idea matters
Circumference measures boundary length and is proportional to diameter through the constant $\pi$.
A dependable method
- Determine whether radius or diameter is given.
- Use $2\pi r$ for radius or $\pi d$ for diameter.
- Keep units consistent and calculate an exact form.
- Approximate with a calculator only if requested.
- Compare with roughly three diameters because $\pi\approx3.14$.
