# What is the general formula to convert radians to degrees and vice versa?

Feb 5, 2016

see explanation

#### Explanation:

$\textcolor{b l u e}{\text{ to convert radians to degrees}}$

( angle in radians) $\times \frac{180}{\pi}$

example: convert $\frac{\pi}{2} \textcolor{b l a c k}{\text{ radians to degrees }}$

angle in degrees $= \frac{\cancel{\pi}}{2} \times \frac{180}{\cancel{\pi}} = \frac{180}{2} = {90}^{\circ}$

$\textcolor{red}{\text{ to convert degrees to radians}}$

(angle in degrees)$\times \frac{\pi}{180}$

example : convert 90º to radians

angle in radians = $\cancel{90} \times \frac{\pi}{\cancel{180}} = \frac{\pi}{2}$