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Unit of measurement of an angle, equal to 1/400th of a circle
"Grade (angle)" redirects here. For the grade of an inclined surface, see
Grade (slope).
In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) 'angle'), grad, or grade[1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.[2][3][4] It is equivalent to 1/400 of a turn,[5] 9/10 of a degree, or π/200 of a radian. Measuring angles in gradians (gons) is said to employ the centesimal system of angular measurement, initiated as part of metrication and decimalisation efforts.[6][7][8][a]
In continental Europe, the French word centigrade, also known as centesimal minute of arc, was in use for one hundredth of a grade; similarly, the centesimal second of arc was defined as one hundredth of a centesimal arc-minute, analogous to decimal time and the sexagesimal minutes and seconds of arc.[12] The chance of confusion was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.[13][14]
Gradians (gons) are principally used in surveying (especially in Europe),[15][7][16] and to a lesser extent in mining[17] and geology.[18][19]
The gon (gradian) is a legally recognised unit of measurement in the European Union[20]: 9 and in Switzerland.[21] However, this unit is not part of the International System of Units (SI).[22][20]: 9–10
The unit originated in France in connection with the French Revolution as the grade, along with the metric system, hence it is occasionally referred to as a metric degree. Due to confusion with the existing term grad(e) in some northern European countries (meaning a standard degree, 1/360 of a turn), the name gon was later adopted, first in those regions, and later as the international standard.[which?] In France, it was also called grade nouveau. In German, the unit was formerly also called Neugrad (new degree) (whereas the standard degree was referred to as Altgrad (old degree)), likewise nygrad in Danish, Swedish and Norwegian (also gradian), and nýgráða in Icelandic.
Although attempts at a general introduction were made, the unit was only adopted in some countries, and for specialised areas such as surveying,[15][7][16] mining[17] and geology.[18][19] Today, the degree, 1/360 of a turn, or the mathematically more convenient radian, 1/2π of a turn (used in the SI system of units) is generally used instead.
In the 1970s –1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their trigonometric functions.[23] In the 2010s, some scientific calculators lack support for gradians.[24]
The international standard symbol for this unit is "gon" (see ISO 31-1, Annex B).[needs update] Other symbols used in the past include "gr", "grd", and "g", the last sometimes written as a superscript, similarly to a degree sign: 50g = 45°. A metric prefix is sometimes used, as in "dgon", "cgon", "mgon", denoting respectively 0.1 gon, 0.01 gon, 0.001 gon. Centesimal arc-minutes and centesimal arc-seconds were also denoted with superscripts c and cc, respectively.
SI multiples of gon (gon) Submultiples Multiples Value SI symbol Name Value SI symbol Name 10−1 gon dgon decigon 101 gon dagon decagon 10−2 gon cgon centigon 102 gon hgon hectogon 10−3 gon mgon milligon 103 gon kgon kilogon 10−6 gon μgon microgon 106 gon Mgon megagon 10−9 gon ngon nanogon 109 gon Ggon gigagon 10−12 gon pgon picogon 1012 gon Tgon teragon 10−15 gon fgon femtogon 1015 gon Pgon petagon 10−18 gon agon attogon 1018 gon Egon exagon 10−21 gon zgon zeptogon 1021 gon Zgon zettagon 10−24 gon ygon yoctogon 1024 gon Ygon yottagon 10−27 gon rgon rontogon 1027 gon Rgon ronnagon 10−30 gon qgon quectogon 1030 gon Qgon quettagon Advantages and disadvantages[edit]Each quadrant is assigned a range of 100 gon, which eases recognition of the four quadrants, as well as arithmetic involving perpendicular or opposite angles.
One advantage of this unit is that right angles to a given angle are easily determined. If one is sighting down a compass course of 117 gon, the direction to one's left is 17 gon, to one's right 217 gon, and behind one 317 gon. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions (as 33+1/3 gon and 66+2/3 gon respectively).
Conversion of common angles Turns Radians Degrees Gradians 0 turn 0 rad 0° 0g 1/72 turn π/36 or 𝜏/72 rad 5° 5+5/9g 1/24 turn π/12 or 𝜏/24 rad 15° 16+2/3g 1/16 turn π/8 or 𝜏/16 rad 22.5° 25g 1/12 turn π/6 or 𝜏/12 rad 30° 33+1/3g 1/10 turn π/5 or 𝜏/10 rad 36° 40g 1/8 turn π/4 or 𝜏/8 rad 45° 50g 1/2π or 𝜏 turn 1 rad 57.3° 63.7g 1/6 turn π/3 or 𝜏/6 rad 60° 66+2/3g 1/5 turn 2π or 𝜏/5 rad 72° 80g 1/4 turn π/2 or 𝜏/4 rad 90° 100g 1/3 turn 2π or 𝜏/3 rad 120° 133+1/3g 2/5 turn 4π or 2𝜏 or α/5 rad 144° 160g 1/2 turn π or 𝜏/2 rad 180° 200g 3/4 turn 3π or ρ/2 or 3𝜏/4 rad 270° 300g 1 turn 𝜏 or 2π rad 360° 400g Relation to the metre [edit] An early definition of the metre was one ten-millionth of the distance from the North Pole to the equator, measured along a meridian through Paris.In the 18th century, the metre was defined as the 10-millionth part of a quarter meridian. Thus, 1 gon corresponds to an arc length along the Earth's surface of approximately 100 kilometres; 1 centigon to 1 kilometre; 10 microgons to 1 metre.[25] (The metre has been redefined with increasing precision since then.)
Relation to the SI system of units [edit]The gradian is not part of the International System of Units (SI). The EU directive on the units of measurement[20]: 9–10 notes that the gradian "does not appear in the lists drawn up by the CGPM, CIPM or BIPM." The most recent, 9th edition of the SI Brochure does not mention the gradian at all.[22] The previous edition mentioned it only in the following footnote:[26]
The gon (or grad, where grad is an alternative name for the gon) is an alternative unit of plane angle to the degree, defined as (π/200) rad. Thus there are 100 gon in a right angle. The potential value of the gon in navigation is that because the distance from the pole to the equator of the Earth is approximately 10000 km, 1 km on the surface of the Earth subtends an angle of one centigon at the centre of the Earth. However the gon is rarely used.
The angle through which the torsion-head must be deflected was measured in centesimal divisions of the circle
German: wurde die Größe der Drehung oben an der Drehwage in Hunderttheilen einer ganzen Umdrehung abgelesen (p. 147) [the amount of rotation at the top of the torsion balance was read in hundred parts of an entire revolution]
It hung on a ribbon torsion element with a knob on top, graduated in 100 parts.
The term "Celsius" was adopted instead of the more familiar "centigrade" because in France the word centigrade has customarily been applied to angles.
On the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC.
On most scientific calculators, this [the unit for angles] is set by the DRG key
Scientific calculators commonly have two modes for working with angles – degrees and radians
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