# What is the radian measure of a right angle?

May 11, 2018

$90$ degrees$= \frac{\pi}{2}$ radians

#### Explanation:

Radians are a unit measure for angles defined as the ratio between the lenght of an arc of circumference and the radius of the circumference itself.

This image from wikipedia explains it quite well:

and this gif helps you understainding why an angle of $180$ degrees translates into $\pi$ radians, and an angle of $360$ degrees translates into $2 \pi$ radians:

That being said, we only need to use some proportions: since a right angle measures $90$ degrees, it is half of a $180$ degrees angle. We already observed that an angle of $180$ degrees translates into $\pi$ radians, and thus an angle of $90$ degrees translates into $\frac{\pi}{2}$ radians (we simply divided by $2$ both the degrees and radians).

May 11, 2018

We have a very goofy system where our circle constant $\pi$ is half a circle, ${180}^{\circ} ,$ so a right angle, one quarter of a circle, ${90}^{\circ}$, is half the circle constant, $\frac{\pi}{2}$. Confused yet?