Please ensure Javascript is enabled for purposes of website accessibility

The distance around a circle is called the circumference. It is similar to the perimeter of a rectangle which is the sum of all its sides. Though the word perimeter is usually reserved for polygons, shapes with straight edges.

To calculate the circumference of a circle, we only need to know its radius. The formula of the circumference is given by $$C = 2\pi r$$ where $$r=$$ radius and pi ($$\pi$$) has a numerical value that is approximately equal to $$3.1416$$. Example 1: What is the circumference of a circle with a radius $$6$$?

Since the radius of the circle is given, we just need to direct substitute that into the formula to get the measure of circumference.

\eqalign{ C &= 2\pi r \cr & = 2\left( \pi \right)\left( \color{red}{6} \right) \cr & = 12\pi \cr}

Therefore, the exact value for the circumference of the circle is $$12\pi$$. Notice that we express our answer in terms of $$\pi$$ if we want to give the exact answer.

However, if we want our answer as an approximation that means we will have to use also a numerical value for $$\pi$$ which in this case is $$3.1416$$.

\eqalign{ C &= 2\pi r \cr & = 2\left( {3.1416} \right)\left( 6 \right) \cr & = 37.6992 \cr}

The circumference is about $$37.7$$, rounded to the nearest tenth.

Example 2: Find the circumference of a circle with a diameter  $$5$$? Round your answer to the nearest hundredth. Use $$\pi=3.1416$$.

Our first step is to determine the radius. Our diameter is given, so we can get the radius by dividing it by $$2$$.

\eqalign{ r &= {1 \over 2}d \cr & = {1 \over 2}\left( 5 \right) \cr & = 2.5 \cr}

Now that we have the radius, we can calculate the circumference of the circle.

\eqalign{ C &= 2\pi r \cr & = 2\left( {3.1416} \right)\left( \color{red}{2.5} \right) \cr & = 15.708 \cr}

Therefore, the circumference is about $$15.71$$ units.