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A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. ^[1] Since one degree is defined as one three hundred sixtieth (1/360) of a circle, 1 MOA is 1/21600 of the amount of arc in a closed circle. It is used in those fields which require a unit for the expression of small angles, such as astronomy or marksmanship. Image File history File links Question_book-3. ... This article is about angles in geometry. ... This article describes the unit of angle. ... For other uses, see Astronomy (disambiguation). ... Shooting is the act of causing a gun to fire at a target. ...

Symbols, abbreviations and subdivisions

The standard symbol for marking the arcminute is the prime (′) (U+2032), though a single quote (') (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is written 1′ (or 1'). It is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it (). This article is not about the symbol for the set of prime numbers, â„™. The prime (′, Unicode U+2032, ′) is a symbol with many mathematical uses: A complement in set theory: A′ is the complement of the set A A point related to another (e. ... Image:ASCII fullsvg There are 95 printable ASCII characters, numbered 32 to 126. ... The circumflex ( ˆ ) (often called a caret, a hat or an uppen) is a diacritic mark used in written Greek, French, Dutch, Esperanto, Norwegian, Romanian, Slovak, Vietnamese, Japanese romaji, Welsh, Portuguese, Italian, Afrikaans and other languages, and formerly in Turkish [citation needed]. It received its English name from Latin circumflexus (bent...

The subdivision of the minute of arc is the second of arc, or arcsecond. There are 60 arcseconds in an arcminute. Therefore, the arcsecond is 1/1296000 of a circle, or (π/648000) radians, which is approximately 1/206265 radian. The symbol for the arcsecond is the double prime (″) (U+2033). To express even smaller angles, standard SI prefixes can be employed; in particular, the milliarcsecond, abbreviated mas, is sometimes used in astronomy. For the musical group, see Radian (band). ... For the musical group, see Radian (band). ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... For other uses, see Astronomy (disambiguation). ...

The sexagesimal system of angular measurement

unit	value	symbol	abbreviations	conversion
degree	1/360 circle	°	deg	17.4532925 mrad
arcminute	1/60 degree	′ (prime)	arcmin, amin, , MOA	290.8882087 µrad
arcsecond	1/60 arcminute	″ (double prime)	arcsec	4.8481368 µrad
milliarcsecond	1/1000 arcsecond		mas	4.8481368 nrad

The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... This article is about angles in geometry. ... This article describes the typographical or mathematical symbol. ... This article is not about the symbol for the set of prime numbers, â„™. The prime (′, Unicode U+2032, ′) is a symbol with many mathematical uses: A complement in set theory: A′ is the complement of the set A A point related to another (e. ...

Uses

Firearms

This unit is commonly found in the firearms industry and literature, particularly that concerning the accuracy of rifles. The industry tends to refer to it as minute of angle rather than minute of arc. It is popular because 1 MOA subtends approximately one inch at 100 yards, a traditional distance on target ranges. A shooter can easily readjust his rifle scope by measuring the distance in inches the bullet hole is from the desired impact point, and adjusting the scope that many MOA in the same direction. Most target scopes designed for long distances are adjustable in quarter (¼) or eighth (⅛) MOA "clicks". One eighth MOA is equal to approximately an eighth of an inch at 100 yards or one inch at 800 yards. A firearm is a kinetic energy weapon that fires either a single or multiple projectiles propelled at high velocity by the gases produced by action of the rapid confined burning of a propellant. ... For other uses, see Rifle (disambiguation). ... In mathematics, subtended usually refers to the direct relationship between an angle and its arc length, or for solid angle the area on a unit sphere cut out by the envelope of the vectors defining the perimeter. ... An inch (plural: inches; symbol or abbreviation: in or, sometimes, ″ - a double prime) is the name of a unit of length in a number of different systems, including English units, Imperial units, and United States customary units. ... A yard (abbreviation: yd) is the name of a unit of length in a number of different systems, including English units, Imperial units, and United States customary units. ... An outdoor shooting range with a sheltered shooting stand and several other unsheltered stands. ... View through a 4x rifle scope A telescopic sight, commonly referred to as a scope, is a device used to give an accurate point of aim for a firearm. ...

Calculating the physical equivalent group size equal to one minute of arc can be done using the equation: equivalent group size = tan(MOA ∕ 60)*distance. In the example previously given and substituting 3600 inches for 100 yards, tan(1 MOA ∕ 60)∙ 3600 inches = 1.0471975511966 inches.

In metric units 1 MOA at 100 meters = 2.90888208665722 centimeters.

Sometimes, a firearm's accuracy will be measured in MOA. This simply means that under ideal conditions, the gun is capable of repeatedly producing a group of shots whose center points (center-to-center) fit into a circle, the diameter of which can be subtended by that amount of arc. (E.g.: a "1 MOA rifle" should be capable, under ideal conditions, of shooting a 1-inch group at 100 yards, a "2 MOA rifle" a 2-inch group at 100 yards, etc.) Some manufacturers such as Weatherby and Cooper offer actual guarantees of real-world MOA performance. Weatherby, Inc. ... Cooper Firearms of Montana was founded in 1990 by Dan Cooper and two other former Kimber of Oregon employees. ...

Rifle manufacturers and gun magazines often refer to this capability as "Sub-MOA", meaning it shoots under 1 MOA. This is typically a single group of 3 to 5 shots at 100 yards, or the average of several groups. If larger samples are taken, i.e. more shots per group, then group size typically increases. ^[2]

Cartography

Minutes of angle (and its subunit, seconds of angle or SOA—equal to a sixtieth of a MOA) are also used in cartography and navigation. At sea level, one minute of angle (around a great circle such as the equator or a meridian) equals about 1.15 miles or 1.86 km, approximately one nautical mile (approximately, because the Earth is slightly oblate). Cartography or mapmaking (in Greek chartis = map and graphein = write) is the study and practice of making maps or globes. ... This article is about determination of position and direction on or above the surface of the earth. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... “Miles” redirects here. ... “km” redirects here. ... A nautical mile or sea mile is a unit of length. ... This article is about Earth as a planet. ... Oblate also refers to a member of the Roman Catholic religious order of the Missionary Oblates of Mary Immaculate, or in some cases to a lay or religious person who has officially associated himself (or herself) with a monastic community such as the Benedictines for reasons of personal enrichment without...

Traditionally positions are given using degrees, minutes, and seconds of angles in two measurements: one for latitude, the angle north or south of the equator; and one for longitude, the angle east or west of the Prime Meridian. Using this method, any position on or above the face of the Earth can be precisely given. However, because of the somewhat clumsy base-60 nature of MOA and SOA, many people now prefer to give positions using degrees only, expressed in decimal form to an equal amount of precision. Degrees, given to three decimal places (1/1000 of a degree), give almost as much precision as degrees-minutes-seconds (1/3600 of a degree). This article is about the geographical term. ... World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses Ilhéu das Rolas, in São Tomé and Príncipe. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... Location of the Prime Meridian Image:Prime Meridian. ...

Property surveying

Related to cartography, property boundary surveying using the metes and bounds system relies on fractions of a degree to describe property lines' angles in reference to cardinal directions. A boundary is described with a beginning reference point, a cardinal direction followed by an angle and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, North 65° 39′ 18″ West 85.69 feet would describe a property line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west. Surveyor at work with a leveling instrument. ... Metes and bounds is a system or method of describing land, real property (in contrast to personal property) or real estate. ... A compass rose showing the cardinal directions Cardinal directions or cardinal points are the four principal directions or points of the compass in plane. ...

Astronomy

The arcminute and arcsecond are also used in astronomy. Degrees (and therefore arcminutes) are used to measure declination, or angular distance north or south of the celestial equator. The arcsecond is also often used to describe parallax, due to very small parallax angles, and tiny angular diameters (e.g. Venus varies between 10″ and 60″). The parallax, proper motion and angular diameter of a star may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The parsec gets its name from "parallax second", for those arcseconds. For other uses, see Astronomy (disambiguation). ... In astronomy, declination (abbrev. ... The celestial equator is a great circle on the imaginary celestial sphere, which could be constructed by inflating the Earths equator until it intersects with said sphere. ... For other uses, see Parallax (disambiguation). ... The proper motion of a star is the motion of the position of the star in the sky (the change in direction in which we see it, as opposed to the radial velocity) after eliminating the improper motions of the stars, which affect their measured coordinates but are not real... A parsec is the distance from the Earth to an astronomical object which has a parallax angle of one arcsecond. ...

From the Earth the star with the largest angular diameter (apart from the Sun) is 0.05 arcsecond and this is a red super giant. Due to 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 angular diameter of an object as seen from a given position is the diameter measured as an angle. ... The word seeing can mean more than one thing: In common usage, the word means visual perception In astronomy, seeing is a technical term related to the blurring effects of air turbulence in the atmosphere In the occult seeing refers to the sight or the ability to see auras or... This article does not cite any references or sources. ...

Space telescopes are not affected by the Earth's atmosphere, but are diffraction limited; for example the Hubble space telescope can reach an angular size of stars down to about 0.1". Techniques exist for improving seeing on the ground, for example adaptive optics, which can give images around 0.05 arcsecond on a 10 m class telescope. Diffraction is the apparent bending and spreading of waves when they meet an obstruction. ... The Hubble Space Telescope (HST) is a telescope in orbit around the Earth, named after astronomer Edwin Hubble. ... A deformable mirror can be used to correct wavefront errors in an astronomical telescope. ...

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. Traditional Snellen chart used for visual acuity testing. ...

References