View source for Radian

[[File:Radian cropped color.svg|250px|thumb|Definition of a radian]]
[[File:Circle_radians.gif|thumb|250px|right|A radian is a unit of angular measure. A revolution of a circle has an angle of 2π radians.]]

A '''radian''' is a unit of measuring [[angle]]s. It is shown by the symbol "rad"<ref>{{Cite web|last=|first=|date=2020-04-17|title=List of Geometry and Trigonometry Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/geometry-trigonometry-symbols/|archive-url=|archive-date=|access-date=2020-08-31|website=Math Vault|language=en-uk}}</ref> or, less often, <sup>c</sup> (for circular measure). The radian was once an [[SI]] [[supplementary unit]], but was changed to a derived unit in 1995. In a circular sector with a central angle of one radian, the arc length is equal to the length of the radius of the circle it is part of.

==Usage==
Most people who do mathematics or physics use radians, rather than [[degree (angle)|degrees]], because some kinds of calculations, mostly in [[trigonometry]] and [[calculus]], are simpler when using radians rather than degrees. Thus, most calculations related to [[angular frequency]] (such as [[angular velocity]]) use radians per second. 

People who look through a [[telescope]] or [[sniper scope]] often use milliradians to describe distances as seen through it.

==Conversion==
1 radian is equal to about 57.3°. There are 2[[Pi (mathematical constant)|π]] radians (about 6.28 radians) in a full revolution.<ref>{{Cite web|title=Radian - math word definition - Math Open Reference|url=https://www.mathopenref.com/radians.html#:~:text=The%20radian%20is%20a%20unit,an%20arc%20of%20a%20circle.|access-date=2020-08-31|website=www.mathopenref.com}}</ref> The formula for converting radians to degrees and vice versa is:<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Radian|url=https://mathworld.wolfram.com/Radian.html|access-date=2020-08-31|website=mathworld.wolfram.com|language=en}}</ref>
:<math>2\pi\mbox{ rad} = 360^\circ</math>
:<math>1 \mbox{ rad} = \frac {360^\circ} {2 \pi} = \frac {180^\circ} {\pi} \approx 57.29577951^\circ </math>

or:

:<math>360^\circ=2\pi\mbox{ rad}</math>
:<math>1^\circ=\frac{2\pi}{360}\mbox{ rad}=\frac{\pi}{180}\mbox{ rad} \approx 0.01745329\mbox{ rad}</math>

we can also say that:

:<math>x \mbox{ rad} = \left(\frac{180x}{\pi}\right)^\circ</math>.

== Related pages ==

* [[Steradian]]
* [[Tau]], the measure of a full circle in radian
* [[Unit circle]]

== References ==
<references />
{{SI units}}

{{math-stub}}

[[Category:Angles]]
[[Category:SI derived units]]