The distance around a circle is its circumference. Every circle, from a coin to a Ferris wheel, follows the same rule, and finding it needs only multiplying decimals.
Key idea
$$C = \pi d = 2\pi r$$ The diameter $d$ goes across through the center; the radius $r$ is half of it. $\pi$ is about $3.14$ (or $\frac{22}{7}$).
Why it works
All circles are the same shape: each is a scaled copy of every other. So the ratio of circumference to diameter is the same for all of them. Roll any circle along a line for one turn: it covers a little more than 3 diameters. That number is $\pi = 3.14159\ldots$; its digits go on forever without repeating, so $3.14$ is only an approximation.
Worked examples
Worked example: From the diameter
A plate has a diameter of 10 inches. Find its circumference.
- $C = \pi d = \pi \times 10 = 10\pi$ inches (exact).
- Using $3.14$: $C \approx 3.14 \times 10 = 31.4$ inches.
Answer: $10\pi \approx 31.4$ inches
Worked example: From the radius
A circle has a radius of 7 cm. Find its circumference. Use $3.14$.
- The diameter is $2 \times 7 = 14$ cm.
- $C \approx 3.14 \times 14 = 43.96$ cm.
Answer: $43.96$ cm
Worked example: Working backward
A circular track is 47.1 m around. What is its diameter? Use $3.14$.
- $C = \pi d$, so $d = C \div \pi$.
- $d \approx 47.1 \div 3.14 = 15$ m.
Answer: 15 m
Common mistake
Using the radius where the formula needs the diameter ($3.14 \times 7 = 21.98$ instead of $43.96$). Check: the circumference is always a little more than 3 times the diameter. Another slip is thinking $\pi$ equals $3.14$ exactly; it only rounds to it.