# How do you convert 16 revolutions to radians?

Aug 28, 2015

You can see that $2 \pi$ radians becomes one revolution when you use the arc length formula:

$s = r \theta$

Let $\theta = 2 \pi$. That means:

$\textcolor{g r e e n}{s = C = 2 \pi r}$

which is the formula for the full circumference of a circle. Since $2 \pi$ radians is one revolution:

16 cancel"rev" xx ((2pi " rad")/(1 cancel"rev")) = color(blue)(32pi " rad")