Explore the circumference of a circle

The circumference is the distance around a circle. If the radius is $r$, then

$C=2\pi r.$

The diameter is $2r$, so the same relationship can also be written as $C=\pi d$.

Interactive model

Change the radius

The circumference grows by 2π units whenever the radius grows by one unit.

Radius: 3.0

Diameter

6.0

Circumference

18.85

C = 2πr = 18.85

What to notice

• Doubling the radius doubles the circumference.
• Increasing the radius by one adds exactly $2\pi$ to the circumference.
• The ratio $C/d$ is always $\pi$, regardless of the circle’s size.

Try it

Set the radius to $2.5$. Predict the circumference before reading the value, then check your calculation using $C=2\pi r$.