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
1/7004216000000000000♠21600 of a turn. A minute of arc is
π/7004108000000000000♠10800 of a radian. A second of arc, arcsecond
(arcsec), or arc second is 1/60 of an arcminute,
1/7003360000000000000♠3600 of a degree,
1/7006129600000000000♠1296000 of a turn, and
π/7005648000000000000♠648000 (about 1/7005206265000000000♠206265)
of a radian. These units originated in
displaystyle 4pi left( frac 10,800 pi right)^ 2 = frac 466,560,000 pi approx
7008148510660000000♠148510660 square arcminutes.
1 Symbols and abbreviations 2 Common examples 3 Uses
3.1 Astronomy 3.2 Cartography 3.3 Property cadastral surveying 3.4 Firearms 3.5 Human vision 3.6 Materials
4 See also 5 Notes 6 References 7 External links
Symbols and abbreviations
The standard symbol for marking the arcminute is the prime (′)
(U+2032), though a single quote (') (U+0027) is commonly used where
displaystyle hat '
The standard symbol for the arcsecond is the double prime (″)
(U+2033), though a double quote (") (U+0022) is commonly used where
Unit Value Symbol Abbreviations In radians, approx.
Degree 1/360 turn ° (degree) deg 7001174532925000000♠17.4532925 mrad
Arcminute 1/60 degree ′ (prime) arcmin, amin, am,
displaystyle hat '
, MOA 6994290888208700000♠290.8882087 μrad
Arcsecond 1/60 arcminute = 1/3600 degree ″ (double prime) arcsec, asec, as 6992484813680000000♠4.8481368 μrad
Milliarcsecond 0.001 arcsecond = 1/3600000 degree
mas 6989484813680000000♠4.8481368 nrad
Microarcsecond 0.001 mas = 6994100000000000000♠0.000001 arcsecond
μas 6986484813679999999♠4.8481368 prad
In celestial navigation, seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the latter format by default. Common examples An arcminute is approximately the resolution of the human eye. An arcsecond is approximately the angle subtended by a U.S. dime coin (18 mm) at a distance of 4 kilometres(about2.5 mi). An arcsecond is also the angle subtended by
an object of diameter 7005725270000000000♠725.27 km at a distance of one astronomical unit, an object of diameter 7010458669160000000♠45866916 km at one light-year, an object of diameter one astronomical unit (7011149597871000000♠149597871 km) at a distance of one parsec.
A milliarcsecond is about the size of a dime atop the
Hubble Space Telescope
Comparison of angular diameter of the Sun, Moon, planets and the International Space Station. True representation of the sizes is achieved when the image is viewed at a distance of 103 times the width of the "Moon: max." circle. For example, if the "Moon: max." circle is 10 cm wide on a monitor, viewing it from 10.3 m away will show true representation of the sizes.
Since antiquity the arcminute and arcsecond have been used in
astronomy. In the ecliptic coordinate system, latitude (β) and
longitude (λ); in the horizon system, altitude (Alt) and azimuth
(Az); and in the equatorial coordinate system, declination (δ), are
all measured in degrees, arcminutes and arcseconds. The principal
exception is right ascension (RA) in equatorial coordinates, which is
measured in time units of hours, minutes, and seconds.
The arcsecond is also often used to describe small astronomical angles
such as the angular diameters of planets (e.g. the angular diameter of
Venus which varies between 10″ and 60″), the proper motion of
stars, the separation of components of binary star systems, and
parallax, the small change of position of a star in the course of a
year or of a solar system body as the Earth rotates. These small
angles may also be written in milliarcseconds (mas), or thousandths of
an arcsecond. The unit of distance, the parsec, named from the
parallax of one arc second, was developed for such parallax
measurements. It is the distance at which the mean radius of the
Earth's orbit would subtend an angle of one arcsecond.
The ESA astrometric space probe Gaia, launched in 2013, can
approximate star positions to 7 microarcseconds (µas).
Apart from the Sun, the star with the largest angular diameter from
Earth is R Doradus, a red supergiant with a diameter of 0.05
arcsecond.[a] Because of the effects of atmospheric seeing,
ground-based telescopes will smear the image of a star to an angular
diameter of about 0.5 arcsecond; in poor seeing conditions this
increases to 1.5 arcseconds or even more. The dwarf planet
Example ballistic table for a given
The arcminute is commonly found in the firearms industry and literature, particularly concerning the accuracy of rifles, though the industry refers to it as minute of angle (MOA). It is especially popular with shooters familiar with the imperial measurement system because 1 MOA is subtended by a sphere with a diameter of 1.047 inches at 100 yards (2.908 cm at 100 m), a traditional distance on U.S. target ranges. The subtension is linear with the distance, for example, at 500 yards, 1 MOA is subtended by a sphere with a diameter of 5.235 inches, and at 1000 yards 1 MOA is subtended by a sphere with a diameter of 10.47 inches. Since many modern telescopic sights are adjustable in half (1/2), quarter (1/4), or eighth (1/8) MOA increments, also known as clicks, zeroing and adjustments are made by counting 2, 4 and 8 clicks per MOA respectively. For example, if the point of impact is 3 inches high and 1.5 inches left of the point of aim at 100 yards (which for instance could be measured by using a spotting scope with a calibrated reticle), the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have a MOA scale printed on them, and even figuring the right number of clicks is relatively easy on scopes that click in fractions of MOA. This makes zeroing and adjustments much easier:
To adjust a 1⁄2 MOA scope 3 MOA down and 1.5 MOA right, the scope needs to be adjusted 3 × 2 = 6 clicks down and 1.5 x 2 = 3 clicks right To adjust a 1⁄4 MOA scope 3 MOA down and 1.5 MOA right, the scope needs to be adjusted 3 x 4 = 12 clicks down and 1.5 × 4 = 6 clicks right To adjust a 1⁄8 MOA scope 3 MOA down and 1.5 MOA right, the scope needs to be adjusted 3 x 8 = 24 clicks down and 1.5 × 8 = 12 clicks right
Another common system of measurement in firearm scopes is the milliradian. Zeroing a mil based scope is easy for users familiar with base ten systems. The most common adjustment value in mil based scopes is 1/10 mil (which approximates 1⁄3 MOA).
To adjust a 1/10 mil scope 0.9 mil down and 0.4 mil right, the scope needs to be adjusted 9 clicks down and 4 clicks right (which equals approximately 3 and 1.5 MOA respectively).
One thing to be aware of is that some MOA scopes, including some
higher-end models, are calibrated such that an
adjustment of 1 MOA on the scope knobs corresponds to exactly 1 inch
of impact adjustment on a target at 100 yards, rather than the
mathematically correct 1.047". This is commonly known as the Shooter's
MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference
between one true MOA and one SMOA is less than half of an inch even at
1000 yards, this error compounds significantly on longer range
shots that may require adjustment upwards of 20-30 MOA to compensate
for the bullet drop. If a shot requires an adjustment of 20 MOA or
more, the difference between true MOA and SMOA will add up to 1 inch
or more. In competitive target shooting, this might mean the
difference between a hit and a miss.
The physical group size equivalent to m minutes of arc can be
calculated as follows: group size = tan(m/60) × distance.
In the example previously given, for 1 minute of arc, and substituting
3,600 inches for 100 yards, 3,600 tan(1/60) ≈
1.047 inches. In metric units 1 MOA at 100 meters ≈ 2.908
Sometimes, a precision firearm's accuracy will be measured in MOA.
This simply means that under ideal conditions i.e. no wind,
match-grade ammo, clean barrel, and a vise or a benchrest used to
eliminate shooter error, the gun is capable of producing a group of
shots whose center points (center-to-center) fit into a circle, the
average diameter of circles in several groups can be subtended by that
amount of arc. For example, a 1 MOA rifle should be capable, under
ideal conditions, of shooting an average 1-inch groups at 100 yards.
Most higher-end rifles are warrantied by their manufacturer to shoot
under a given MOA threshold (typically 1 MOA or better) with specific
ammunition and no error on the shooter's part. For example,
M24 Sniper Weapon System
Comparison of milliradian (mil) and minute of arc (moa).
Conversion between common sight adjustments based on milliradian and minute of arc
Angle adjustment per click Minute of arc equivalent Mil equivalent mm at 100 m cm at 100 m in at 100 m in at 100 yd
1⁄12′ 0.083′ 0.024 mil 2.42 mm 0.242 cm 0.0958 in 0.087 in
0.25⁄10 mil 0.086′ 0.025 mil 2.5 mm 0.25 cm 0.0985 in 0.09 in
1⁄8′ 0.125′ 0.036 mil 3.64 mm 0.36 cm 0.144 in 0.131 in
1⁄6′ 0.167′ 0.0485 mil 4.85 mm 0.485 cm 0.192 in 0.175 in
0.5⁄10 mil 0.172′ 0.05 mil 5 mm 0.5 cm 0.197 in 0.18 in
1⁄4′ 0.25′ 0.073 mil 7.27 mm 0.73 cm 0.29 in 0.26 in
1⁄10 mil 0.344′ 0.1 mil 10 mm 1 cm 0.39 in 0.36 in
1⁄2′ 0.5′ 0.145 mil 14.54 mm 1.45 cm 0.57 in 0.52 in
1.5⁄10 mil 0.516′ 0.15 mil 15 mm 1.5 cm 0.59 in 0.54 in
2⁄10 mil 0.688′ 0.2 mil 20 mm 2 cm 0.79 in 0.72 in
1′ 1.0′ 0.291 mil 29.1 mm 2.91 cm 1.15 in 1.047 in
1 mil 3.438′ 1 mil 100 mm 10 cm 3.9 in 3.6 in
(Values in bold face are exact. All mil fractions are given in tenths, which is more convenient for practical use.)
1′ at 100 yards equals 22619/ 21600 = 1.04717593 in ≈ 1.047 inches 1′ ≈ 0.291 mil (or 2.91 cm at 100 m, approximately 3 cm at 100 m) 1 mil ≈ 3.44′, so 1/10 mil ≈ 1/3′ 0.1 mil equals exactly 1 cm at 100 m, or approximately 0.36 inches at 100 yards
Human vision In humans, 20/20 vision is the ability to resolve a spatial pattern separated by a visual angle of one minute of arc. A 20/20 letter subtends 5 minutes of arc total. Materials The deviation from parallelism between two surfaces, for instance in optical engineering, is usually measured in arcminutes or arcseconds. In addition, arcseconds are sometimes used in rocking curve (ω-scan) x ray diffraction measurements of high-quality epitaxial thin films. See also
^ Some studies have shown a larger angular diameter for Betelgeuse.
Various studies have produced figures of between 0.042 and 0.069
arcseconds for the star's diameter. The variability of
^ a b "ASME Y14.5-2009 Dimensioning" (PDF). Retrieved 22 February
^ "CELESTIAL NAVIGATION COURSE". International
MOA / mils By Robert Simeone
v t e
International System of Units
ampere candela kelvin kilogram metre mole second
Derived units with special names
becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber
Other accepted units
astronomical unit bar dalton day decibel degree of arc electronvolt hectare hour litre minute minute of arc neper second of arc tonne atomic units natural units
Conversion of units Metric prefixes Proposed redefinitions Systems of measurement