Grad (angle)

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The grad is a unit of plane angle, equivalent to ¹⁄₄₀₀ of a full circle, dividing a right angle in 100. It is also known as gon, grade, or gradian (not to be confused with grade of a slope, gradient, or radian). One grad equals ⁹⁄₁₀ of a degree or ^π⁄₂₀₀ of a radian. In continental Europe, the term centigrade was in use for one hundredth of a grade, and the term myriograde was in use for one ten-thousandth of a grade. This was one reason for the adoption of the term centigrade for the unit of temperature.

One advantage of this unit is that right angles are easy to add and subtract in mental arithmetic. If one is travelling on a course of 117 grad (clockwise from due North), say, then the direction to one's left is instantly convertible into 17 grads, while that to one's right is at 217 grads and that behind one is at 317 grads. Another advantage is that 1 grad of a great circle course on the surface of the Earth corresponds to 100 km distance. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions (33¹⁄₃ grad and 66²⁄₃ grad, respectively). Similarly, in one hour (¹⁄₂₄ day), Earth rotates by 15° or 16²⁄₃ grad.

The unit originated in France as the grade, along with the metric system. Due to confusion with existing grad(e) units of northern Europe, the name gon was later adopted, first in those regions, later as the international standard. In German, the unit was formerly also called Neugrad (new degree).

Although attempts at a general introduction were made, the unit was really only adopted in some countries and for specialized areas, like surveying. The French artillery has used the grad for decades. The degree, ¹⁄₃₆₀ of a circle, or the mathematically convenient radian, ¹⁄_(2π) of a circle (used in the SI system of units) are generally used instead. In the '70s and '80s most scientific calculators offered the grad as well as radians and degrees for their trigonometric functions, but in recent years some offered degrees and radians only.

The international standard symbol for this unit today is "gon" (see ISO 31-1). Other symbols used in the past include "gr", "grd", and "g", the latter sometimes written as a superscript, similarly to a degree sign: 50^g = 45°.

[edit] Other meanings

The name gon has also been used in Vietnam for a dimension of 195 metres (approximately 213 yards), and in Persia for a unit of mass originally equal to 0.045 grammes, and later to 0.048 grammes.