In trigonometry, the gradianalso known as the gon (), grad, or gradeis a

unit of measurement A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other qua ...

of an

angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...

, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees. It is equivalent to of a turn, of a degree, or of a

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...

. Measuring angles in gradians (gons) is said to employ the ''centesimal'' system of angular measurement, initiated as part of

metrication Metrication or metrification is the act or process of converting to the metric system of measurement. All over the world, countries have transitioned from local and traditional Unit of measurement, units of measurement to the metric system. This ...

and decimalisation efforts. In continental

Europe Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and Asia to the east ...

, 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. The chance of confusion was one reason for the adoption of the term '' Celsius'' to replace ''centigrade'' as the name of the temperature scale. Gradians (gons) are principally used in surveying (especially in Europe), and to a lesser extent in mining and

geology Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth ...

. The gon (gradian) is a legally recognised unit of measurement in the

European Union The European Union (EU) is a supranational union, supranational political union, political and economic union of Member state of the European Union, member states that are Geography of the European Union, located primarily in Europe. The u ...

and in

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

. However, this unit is not part of the International System of Units (SI).

History and name

The unit originated in

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

in connection with the French Revolution as the , along with the

metric system The metric system is a system of measurement that standardization, standardizes a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative unit prefixes. Though the rules gover ...

, 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, of a turn), the name ''gon'' was later adopted, first in those regions, and later as the international standard. In France, it was also called . In German, the unit was formerly also called (new degree) (whereas the standard degree was referred to as (old degree)), likewise in Danish, Swedish and Norwegian (also ''gradian''), and 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, mining and

. Today, the degree, of a turn, or the mathematically more convenient

, of a turn (used in the SI system of units) is generally used instead. In the 1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their

trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...

. In the 2010s, some scientific calculators lack support for gradians.

Symbol

The international standard symbol for this unit is "gon" (see ISO 31-1, Annex B). Other symbols used in the past include "gr", "grd", and "g", the last sometimes written as a superscript, similarly to a degree sign: 50^g = 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.

Advantages and disadvantages

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 gon and gon respectively).

Conversion

Relation to the metre

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.Cartographie – lecture de carte – Partie H Quelques exemples à retenir
. (The metre has been redefined with increasing precision since then.)

Relation to the SI system of units

The gradian is ''not'' part of the International System of Units (SI). The EU directive on the units of measurement 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. The previous edition mentioned it only in the following footnote:

Notes

References

{{Reflist

External links

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Units of plane angle Decimalisation Metrication Non-SI metric units