Editing Radian (section)

== Conversions ==
{{Table of angles|float=right}}

=== Between degrees ===
As stated, one radian is equal to <math>{180^\circ}/{\pi}</math>. Thus, to convert from radians to degrees, multiply by <math>{180^\circ}/{\pi}</math>.

:<math> \text{angle in degrees} = \text{angle in radians} \cdot \frac {180^\circ} {\pi}</math>

For example:
:<math>1 \text{ rad} = 1 \cdot \frac {180^\circ} {\pi} \approx 57.2958^\circ </math>
:<math>2.5 \text{ rad} = 2.5 \cdot \frac {180^\circ} {\pi} \approx 143.2394^\circ </math>
:<math>\frac {\pi} {3} \text{ rad} = \frac {\pi} {3} \cdot \frac {180^\circ} {\pi} = 60^\circ </math>

Conversely, to convert from degrees to radians, multiply by <math>{\pi}/{180} \text{ rad}</math>.

:<math> \text{angle in radians} = \text{angle in degrees} \cdot \frac {\pi} {180} \text{ rad}</math>

For example:

:<math>1^\circ = 1 \cdot \frac {\pi} {180} \text{ rad}\approx 0.0175 \text{ rad}</math>
<math>23^\circ = 23 \cdot \frac {\pi} {180} \text{ rad}\approx 0.4014 \text{ rad}</math>

Radians can be converted to [[Turn (geometry)|turns]] (one turn is the angle corresponding to a revolution) by dividing the number of radians by 2{{pi}}.

=== Between gradians ===

One revolution is <math>2\pi</math> radians, which equals one [[turn (unit)|turn]], which is by definition 400 [[gradian]]s (400 [[gon (unit)|gon]]s or 400<sup>g</sup>). To convert from radians to gradians multiply by <math>200^\text{g}/\pi</math>, and to convert from gradians to radians multiply by <math>\pi/200 \text{ rad}</math>. For example,
:<math>1.2 \text{ rad} = 1.2 \cdot \frac {200^\text{g}} {\pi} \approx 76.3944^\text{g}</math>
:<math>50^\text{g} = 50 \cdot \frac {\pi} {200} \text{ rad}\approx 0.7854 \text{ rad}</math>