Circles and Circumference

In short: The circumference is the distance around a circle: $C=\pi d$, where $d$ is the diameter (twice the radius) and $\pi \approx \frac{22}{7}$ or 3.14. A quick estimate is that the circumference is about 3 diameters.

Before you start

• Perimeter is the distance around a shape.
• Multiplying by a fraction: $\frac{22}{7}\times 14=22\times 2=44$.
• Multiplying decimals: $3.14\times 10=31.4$.

Parts of a circle

Estimating: about 3 diameters

Going backwards: if the circumference is about 42 cm, the radius is about $42÷6=7$ cm.

The exact formula

$\frac{22}{7}=3\frac{1}{7}$, which is just a bit more than 3. It is a little more accurate than $3.14$. Use whichever the question tells you.

Quick summary

• The radius goes from the centre to the edge. The diameter goes right across, and $d=2r$.
• Circumference is the distance around a circle.
• Estimate: $C$ is about 3 diameters or 6 radii.
• Exact: $C=\pi d$, with $\pi \approx \frac{22}{7}$ or $3.14$.
• Use $\frac{22}{7}$ when the diameter is a multiple of 7.
• If you are given the radius, double it first.

Quiz