In trigonometry, the gradianalso known as the gon (), grad, or gradeis 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. It is equivalent to of a turn, of a degree, or 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.

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. 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),

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and to a lesser extent in mining and geology.

The gon (gradian) is a legally recognised unit of measurement in the European Union and in Switzerland. However, this unit is not part of the International System of Units (SI). In the 2010s, some scientific calculators<!-- from Texas Instruments and at least one from Hewlett-Packard --> 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<sup>g</sup> = 45°.

A metric prefix is sometimes used, as in "dgon", "cgon", "mgon", denoting respectively 0.1&nbsp;gon, 0.01&nbsp;gon, 0.001&nbsp;gon.

Centesimal arc-minutes and centesimal arc-seconds were also denoted with superscripts <sup>c</sup> and <sup>cc</sup>, respectively.

Advantages and disadvantages

Each quadrant is assigned a range of 100&nbsp;gon, which eases recognition of the four quadrants, as well as arithmetic involving perpendicular or opposite angles.

: {|

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|align="right"| 0° ||align="center"| = ||align="right"| 0 gradians

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|align="right"| 90° ||align="center"| = ||align="right"| 100 gradians

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|align="right"| 180° ||align="center"| = ||align="right"| 200 gradians

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|align="right"| 270° ||align="center"| = ||align="right"| 300 gradians

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|align="right"| 360° ||align="center"| = ||align="right"| 400 gradians

|}

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&nbsp;gon, the direction to one's left is 17&nbsp;gon, to one's right 217&nbsp;gon, and behind one 317&nbsp;gon. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions (as &nbsp;gon and &nbsp;gon respectively).

Conversion

Relation to the metre <span class="anchor" id="Metre"></span>

thumb|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&nbsp;gon corresponds to an arc length along the Earth's surface of approximately 100&nbsp;kilometres; 1&nbsp;centigon to 1&nbsp;kilometre; 10&nbsp;microgons to 1&nbsp;metre. (The metre has been redefined with increasing precision since then.)

Relation to the SI system of units <span class="anchor" id="SI"></span>

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

See also

  • (primarily military use)
  • (the "square radian")

Notes

References

  • Ask Dr Math
  • Definitions of grade, gon and centigrade on sizes.com
  • Dictionary of Units