I came across this, maybe it can confuse things a little more ?
Minute and Second of Arch:
Not to be confused with
Milliradian.
This article is about arcsec (unit of angle). For the inverse function, see
arcsec (trigonometric function).
Arcminute
An illustration of the size of an arcminute. A standard
association football ball (22 cm diameter) subtends an angle of 1 arcminute at a distance of approximately 775 meters.
Unit information
Unit system Non-SI units mentioned in the SI
Unit of Angle
Symbol ′ or arcmin
In units Dimensionless with an arc length of approx. ≈ 0.2908/1000 of the radius, i.e. 0.2908 mm/m
Unit conversions
1 ′ in ... ... is equal to ...
degrees 1/60° = 0.016°
arcseconds 60′′
radians π/10800 ≈ 0.000290888 rad
milliradians ≈ 0.2908 mil
gons 600/9g = 66.6g
turns 1/21600
A
minute of arc,
arcminute (arcmin),
arc minute, or
minute arc is a unit of
angular measurement equal to 1/60 of one
degree. Since one degree is 1/360 of a
turn (or complete rotation), one minute of arc is 1/21600 of a turn. A minute of arc is π/10800 of a
radian. A
second of arc,
arcsecond (arcsec), or
arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 (about 1/206265) of a radian. These units originated in
Babylonian astronomy as
sexagesimal 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.
The number of square arcminutes in a complete sphere is 4π(10800π)2=466560000π≈
148510660 square arcminutes (the surface area of a unit sphere in square units divided by the solid angle area subtended by a square arcminute, also in square units - so that the final result is a dimensionless number).
