What Are Degrees and Radians?

Degrees and radians measure angles

Degrees and radians are both ways to write out angle measurements.

Degrees are more common in general: there are $360$ degrees in a whole circle, $180$ degrees in a half circle, and $90$ degrees in a quarter of a circle (a right angle). We use a little circle next to a number to indicate we're talking about degrees: $360^\circ, 180^\circ, 90^\circ,$ etc.

A radian is the amount an angle has to open such that the length of the section of the circle's circumference it captures is equal to the length of the radius.

There are $2\pi$ radians in a whole circle, which means that half a circle (180°) is equal to $\pi$ radians. This comparison means that: $$360^\circ = 2\pi \text{ radians}\\\ \\ 180^\circ = \pi \text{ radians}\\\ \\ 90^\circ = \frac{\pi}{2} \text{ radians}\\\ \\ 60^\circ = \frac{\pi}{3} \text{ radians}\\\ \\ 45^\circ = \frac{\pi}{4} \text{ radians}$$ ... and so on.