# Degree to Radian Measure

The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. In radians, one complete counterclockwise revolution is
$2\pi $
and in degrees, one complete counterclockwise revolution is
$360\xb0$
. So,
degree measure
and
radian measure
are related by the equations

$360\xb0=2\pi \text{radians}$

and

$180\xb0=\pi \text{radians}$

From the latter, we obtain the equation $1\xb0=\frac{\pi}{180}\text{radians}$ . This leads us to the rule to convert degree measure to radian measure. To convert from degrees to radians, multiply the degrees by $\frac{\pi}{180\xb0}\text{radians}$ .

**
Example 1:
**

Convert $60\xb0$ to radian measure.

$\left(60\xb0\right)\left(\frac{\pi}{180\xb0}\text{rad}\right)=\frac{\pi}{3}\text{rad}$

**
Example 2:
**

Convert $150\xb0$ to radian measure.

$\left(150\xb0\right)\left(\frac{\pi}{180\xb0}\text{rad}\right)=\frac{5\pi}{6}\text{rad}$