Lesson 39: Circumference of a Circle

New Concept

A circle's circumference is the distance around its edge—like the crust on a pizza. No matter the circle's size, its circumference has a special relationship with its diameter (the distance across). This connection is defined by a unique number called pi ($\pi$).

What’s next

You will learn the key formulas that connect circumference, diameter, and radius. We'll also explore practical approximations for $\pi$ (like $3.14$ and $\frac{22}{7}$) to make calculations a breeze.

Property

To find a circle's circumference, use the formulas $c = \pi d$ or $c = 2\pi r$.

Examples

A pizza with a 14-inch diameter has a circumference of $c = \pi \cdot 14 = 14\pi$ inches.
A tire with a 13-inch radius has a circumference of $c = 2\pi \cdot 13 = 26\pi$ inches.

Explanation

Imagine unrolling a circle into a straight line—that's the circumference! It is always pi ($\pi$) times the diameter. This trick works for any circle, big or small. Just multiply the diameter by $\pi$ to find the distance around it, like measuring the delicious crust on a pizza.

Property

Since $\pi$ is an irrational number, we use approximations for calculations: $\pi \approx 3.14$ and $\pi \approx \frac{22}{7}$.

Examples

For a 10-foot diameter pool, use 3.14: $c \approx 3.14 \cdot 10 = 31.4$ feet.
For a 21-meter diameter crater, use $\frac{22}{7}$: $c \approx \frac{22}{7} \cdot 21 = 66$ meters.

Explanation

Pi's decimals go on forever, so we use handy stand-ins. The decimal 3.14 is a great all-purpose choice. But if your diameter is a multiple of 7, use the fraction $\frac{22}{7}$ to make canceling out numbers a breeze and simplify your work.

Property

The diameter ($d$) is the full distance across a circle's center, while the radius ($r$) is half that distance. The formulas are $d=2r$ and $r = \frac{d}{2}$.

Examples

A clock face with a radius of 6 inches has a diameter of $d = 2 \cdot 6 = 12$ inches.
A rug with a diameter of 8 feet has a radius of $r = \frac{8}{2} = 4$ feet.

Explanation

Think of a pizza! The diameter is the long cut across the middle. The radius is just half that distance, from the center to the crust. If you know one, you can always find the other.