The gradian is a unit of plane angle, equivalent to 1400 of a turn.[1]

It is also known as gon, grad, or grade. One grad equals 910 of a degree or π200 of a radian. In continental Europe, the French term centigrade was in use for one hundredth of a grad, and the term myriograde was in use for one ten-thousandth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.[2][3]

## History

The unit originated in France as the grade, along with the metric system, hence it is occasionally referred to a "metric degree." 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), likewise Nygrad in Swedish, Danish 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. The French artillery has used the grad for decades. The degree, 1360 of a circle, or the mathematically more convenient radian, 1(2π) of a circle (used in the SI system of units) are generally used instead.

In the 1970s and 80s most scientific calculators offered the grad as well as radians and degrees for their trigonometric functions[4] In the 2010s most scientific calculators have tended to offer degrees and radians only, but retained the ability to convert to Grad.[5]

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 last sometimes written as a superscript, similarly to a degree sign: 50g = 45°. "Grad" was commonly used on calculators with LCD displays, as "DEG", "GRAD", and "RAD" could all be represented as a subsection of a panel with the letters "DEGRAD".

## Benefits

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 grad, the direction to one's left is 17 grad, to one's right 217 grad and behind one 317 grad. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions (3313 grad and 6623 grade, respectively). Similarly, in one hour (124 day), Earth rotates by 15° or 1623 gon.

Originally, 1 gradians of arc along the Earth's surface was equal to 100 kilometers of distance at the equator; therefore 1 centigrad of arc equals 1 kilometer.[6]

Gradians are also convenient when working with vectors on the complex plane. The exponent of the imaginary unit on any given vector is equal to its angle (argument) in hectogradians (100 grad) from the positive x-axis: $i^n$ has an argument of $100n$ grade.

## Use in surveying

In surveying, the gradian is the default unit of angles in many parts of the world.[7] Subdivisions of gradian used in surveying can be referred to as c and cc (1 c = 0.01 grad; 1 cc = 0.0001 grad).

## Conversion of some common angles

Units Values
Turns   0 1/24 1/12 1/10 1/8 1/(2π) 1/6 1/5 1/4 1/3 2/5 1/2 3/4 1
Radians 0 π/12 π/6 π/5 π/4 1 π/3 2π/5 π/2 2π/3 4π/5 π 3π/2 2π
Degrees   15° 30° 36° 45° 57.3° 60° 72° 90° 120° 144° 180° 270° 360°
Gon 0g 162/3g 331/3g 40g 50g 63.7g 662/3g 80g 100g 1331/3g 160g 200g 300g 400g