# Circumference of a Circle

Formula for circumference with examples

#### What is circumference anyway?

Answer: The circumference of a circle is the edge or rim of a circle itself. It is the equivalent of 'perimeter' for a circle. In other words, if you took a circle and unrolled it, you would have its circumference. You can use either of the formulas below to find the circumference . One formula use the radius of a circle; the other formula uses the diameter.

#### What is the formula for circumference?

 Formula using Diameter Formula using Radius $$Circumference = \pi \cdot diameter$$ $$Circumference = 2\pi\cdot radius$$

**These two formulas are just two different ways of finding the same thing (circumference) because the diameter of a circle =2• radius. So you can use whichever formula is more convenient. If you know a circle's radius, use the first version of the formula; if you know the diameter, use the second

### The Circle Song

The rotating line on the left is an example of a circle's radius.

If the radius of a circle is 1 inch (1"), then the circumference of the circle = 2 Π • 1" ≈   6.28 "

### Practice Problems

\eqalignno{ Circumference &= 2\pi\cdot radius \\ &= 2\pi\cdot 15 \\ &= \pi\cdot 30 \\ &=94}

\eqalignno{ Circumference &= 2\pi\cdot radius \\ &=2\pi\cdot 9 \\ &=18\pi \\ &= 56.5}

\eqalignno{ Circumference &= 2\pi\cdot radius \\ &=2\pi\cdot 71 \\ &=142\pi \\ &= 446}

Since they gave us the diameter in this picture, use the diameter version of the formula.

\eqalignno{ Circumference &= \pi\cdot diameter \\ &= 13\pi \\ &= 40.8}

### Challenge Problems

Since they gave us the diameter in this picture, use the radius version of the formula

\eqalignno{ Circumference &= 2\pi\cdot radius \\ &=2\pi\cdot 5 \\ &=10\pi \\ &= 31.4}

Since they gave us the diameter in this picture, use the radius version of the formula

\eqalignno{ Circumference &= 2\pi\cdot radius \\ 22\pi &=2\pi\cdot r \\ \frac{22\pi}{\pi} &= \frac{2\pi\cdot r}{\pi} \\ 22 &= 2\cdot r \\ \frac{22}{2} &= r \\ r &= 11 \text{ inches }}

Since they gave us the diameter in this picture, use the radius version of the formula

\eqalignno{ Circumference &= \pi\cdot diameter \\ 102 &= \pi\cdot diameter \\ \frac{102}{\pi} &= \frac{\pi\cdot diameter}{ \pi} \\ 32.5 &= diameter }