Editing Minute and second of arc (section)

{{Short description|Units for measuring angles}}
{{For|the SI units of angle|radian|milliradian}}
{{redirect|Arcsec|the arcsecant function|Inverse trigonometric functions}}
{{about|divisions of a degree of angle|divisions of an hour of angle|hour angle}}
{{More citations needed|date=March 2022}}
{{Use dmy dates|date=July 2019}}
{{Infobox unit
| name         = Arcminute
| image        = Arcminute and football.png
| caption      = An illustration of the size of an arcminute (not to scale). A standard [[Ball (association football)|association football (soccer) ball]] (with a diameter of {{cvt|22|cm|in|disp=or}}) subtends an angle of 1 arcminute at a distance of approximately {{cvt|756|m|yd}}.
| standard     = [[Non-SI units mentioned in the SI]]
| quantity     = [[Angle]]
| symbol       = [[Prime (symbol)|′]]
| symbol2      = arcmin
| namedafter   =
| extralabel   = In units
| extradata    = [[Dimensionless quantity|Dimensionless]] with an [[arc length]] of approx. ≈ {{sfrac|0.2909|1000}} of the radius, i.e. 0.2909 {{sfrac|mm|m}}
| units1 = [[Degree (angle)|degrees]]
| inunits1     = {{sfrac|1|60}}° = 0.01{{overline|6}}°
| units2 = [[arcsecond]]s
| inunits2     = 60″
| units3 = [[radian]]s
| inunits3     = {{sfrac|{{pi}}|10800}} ≈ 0.000290888 rad
| units4 = [[milliradian]]s
| inunits4     = {{sfrac|5{{pi}}|54}} ≈ 0.2909&nbsp;mrad
| units5 = [[gradian]]s
| inunits5     = {{sfrac|3|200}}<sup>g</sup> = 0.015<sup>g</sup>
| units6 = [[Turn (angle)|turns]]
| inunits6     = {{sfrac|1|21600}} turn
}} 
A '''minute of arc''', '''arcminute''' (abbreviated as '''arcmin'''), '''arc minute''', or '''minute arc''', denoted by the symbol {{char|′}}, is a unit of [[Angular unit|angular]] measurement equal to {{sfrac|1|60}} of a [[Degree (angle)|degree]].<ref name=":2">{{Cite web |last=Weisstein|first=Eric W.|title=Arc Second |url=https://mathworld.wolfram.com/ArcSecond.html|access-date=2020-08-31|website=mathworld.wolfram.com |language=en}}</ref><!-- DO NOT USE THIS SITE TO SUPPORT THE DESIGNATION OF SYMBOLS FOR THE ARCMINUTE AND ARCSECOND. It uses the apostrophe for the arcminute and two apostrophes for the arcsecond rather than the prime and double prime. --> Since one degree is {{sfrac|1|360}} of a [[turn (geometry)|turn, or complete rotation]], one arcminute is {{sfrac|1|{{val|21,600}}}} of a turn. The [[nautical miles|nautical mile]] (nmi) was originally defined as the [[meridian arc|arc length]] of a minute of latitude on a spherical Earth, so the actual [[Earth's circumference]] is very near {{val|21,600|u=nmi}}. A minute of arc is {{sfrac|{{pi}}|{{val|10,800}}}} of a [[radian]].

A '''second of arc''', '''arcsecond''' (abbreviated as '''arcsec'''), or '''arc second''', denoted by the symbol {{char|″}},<ref name=":3">{{Cite web|title=Minutes of Arc to Degree Conversion |url=https://www.inchcalculator.com/convert/arcminute-to-degree/ |access-date=2021-07-25|website=Inch Calculator |language=en}}</ref> is a unit of [[Angular unit|angular]] measurement equal to {{sfrac|1|60}} of a minute of arc, {{sfrac|1|{{val|3,600}}}} of a degree,<ref name=":2"/> {{sfrac|1|{{val|1,296,000}}}} of a turn, and {{sfrac|{{pi}}|{{val|648,000}}}} (about {{sfrac|1|{{val|206,264.8}}}}) of a radian.

These units originated in [[Babylonian astronomy]] as [[sexagesimal]] (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as [[astronomy]], [[optometry]], [[ophthalmology]], [[optics]], [[navigation]], [[land surveying]], and [[marksmanship]].

To express even smaller angles, standard [[SI prefixes]] can be employed; the '''milliarcsecond''' (mas) and '''microarcsecond''' (μas), for instance, are commonly used in astronomy. For a two-dimensional area such as on (the surface of) a [[sphere]], ''[[square arcminutes]]'' or ''seconds'' may be used.