Editing Radian (section)

{{short description|SI derived unit of angle}}
{{redirect-distinguish|{{not a typo|㎭}}|Rad (radiation unit)}}
{{other uses|Radian (disambiguation)}}
{{pp-semi-indef}}
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{{Infobox unit
| name          = Radian
| image         = Circle radians.gif
| caption       = An arc of a [[circle]] with the same length as the [[radius]] of that circle subtends an ''angle'' of 1&nbsp;radian. The circumference subtends an angle of 2{{math|[[pi|&pi;]]}} radians.
| standard      = [[International System of Units|SI]]
| quantity      = [[angle]]
| symbol        = rad
| symbol4       = {{sup|R}}<ref name="Hall_1909"/>
| units1        = [[milliradian]]s
| inunits1      = 1000 mrad
| units2        = [[Turn (angle)|turn]]s
| inunits2      = {{sfrac|1|2{{pi}}}} turn ≈ 0.159154 turn
| units3        = [[Degree (angle)|degree]]s
| inunits3      = {{sfrac|180|{{pi}}}}° ≈ 57.295779513°
| units4        = [[gradian]]s
| inunits4      = {{sfrac|200|{{pi}}}}&nbsp;grad ≈ 63.661977<sup>g</sup>
}}

The '''radian''', denoted by the symbol '''rad''', is the unit of [[angle]] in the [[International System of Units]] (SI) and is the standard unit of angular measure used in many areas of [[mathematics]]. It is defined such that one radian is the angle subtended at the centre of a circle by an [[Circular arc|arc]] that is equal in length to the radius.<ref name="DDUnits"/> The unit was formerly an [[SI supplementary unit]] and is currently a [[dimensionless unit|dimensionless]] [[SI derived unit]],<ref name="DDUnits">{{harvnb|International Bureau of Weights and Measures|2019|p=151}}: "The CGPM decided to interpret the supplementary units in the SI, namely the radian and the steradian, as dimensionless derived units."</ref> defined in the SI as 1 rad = 1<ref>{{harvnb|International Bureau of Weights and Measures|2019|p=151}}: "One radian corresponds to the angle for which s = r, thus 1 rad = 1."</ref> and expressed in terms of the [[SI base unit]] [[metre]] (m) as {{nobr|1=rad = m/m}}.{{sfn|International Bureau of Weights and Measures|2019|p=137}} Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.<ref>{{cite book |title=Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3 |date=2002 |publisher=National Aeronautics and Space Administration, Goddard Space Flight Center |page=12 |url=https://books.google.com/books?id=Bo0eAQAAIAAJ&pg=PA12 |language=en}}</ref>