# How do you convert -pi radians to degrees?

Sep 7, 2015

$- \pi$ radians is $180$ degrees.

#### Explanation:

$1$ degree is equal to $\frac{\pi}{180}$ radians.

$1$ radian is equal to $\frac{180}{\pi}$ degrees.

From here we can see that $\pi$ radians is $180$ degrees.

Remember that negative angles are angles that go clockwise.

$\pi$ radians is the same as $- \pi$ radians because going $180$ degrees counterclockwise is the same as going $180$ degrees clockwise. You can imagine this.

Therefore $- \pi$ radians is $180$ degrees.

For angles in general, $- r$ radians is the same angle as $2 \pi - r$ radians. Similarly, $- r$ degrees is the same angle as $360 - r$ degrees. You can do this if you want to work with positive angles.