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### Grad as a Measure of an Angle

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Date: 03/20/2002 at 13:39:52
From: Evelyn Benoit
Subject: Grad as a Measure of an Angle

a full rotation and may have been used by the British military.

I would like to know more about its origins, its use in the past, and
whether (and how) it is used now.

Some of my students have also looked and have been unable to find

Thank you,
Evelyn Benoit
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Date: 03/20/2002 at 17:00:13
From: Doctor Peterson
Subject: Re: Grad as a Measure of an Angle

Hi, Evelyn.

There is some information about it in Russ Rowlett's _How Many?_, a
dictionary of units listed in our FAQ:

http://www.unc.edu/~rowlett/units/dictG.html

a unit of angle measurement equal to 1/400 circle, 0.01 right angle,
0.9 degrees, or 54'. This unit was introduced in France, where it is
called the grade, in the early years of the metric system. The grad
is the English version, apparently introduced by engineers around
1900. The name gon is used for this unit in German, Swedish, and
other northern European languages in which the word grad means
degree. Although many calculators will display angle measurements in
grads as well as degrees or radians, it is difficult to find actual

There is also a little information in Jeff Miller's Earliest Uses of
Words of Mathematics, also listed in our FAQ:

http://jeff560.tripod.com/g.html

GRAD or GRADE originally meant one ninetieth of a right angle, but
the term is now used primarily to refer to one hundredth of a right
angle.

Gradus is a Latin word equivalent to "degree."

Nicole Oresme called the difference between two successive
latitudines a gradus (Smith vol. 2, page 319).

The OED2 shows a use of grade in English in about 1511, referring
to one-ninetieth of a right angle.

The OED2 shows a use of grade, meaning one-hundredth of a right
angle, in 1801 in Dupre Neolog. Fr. Dict. 127: "Grade .. the
grade, or decimal degree of the meridian."

The term may have been used in the modern sense in the unpublished

In 1857, Mathematical Dictionary and Cyclopedia of Mathematical
Science has: "The French have proposed to divide the right angle
into 100 equal parts, called grades, but the suggestion has not

Searching for other references, I found these:

NIMA: Datums, Ellipsoids, Grids, and Grid Reference Systems
http://cartome.org/nima-grids.htm

Some foreign produced maps may use the centesimal (decimal) system
of angular measurement (the division of a full circle into 400
seconds).
...
Geographic coordinates are given in terms of angular measurement,
usually in degrees, minutes, and seconds but occasionally in grads.

Gregor Shapiro helped me find this one:

Silva: General Compass InformationReference Systems
http://www.silva.se/outdoor/products/comp_general.htm

Normal graduation is 360o. For Scandinavian countries 400 gon
is also used. Military graduation 6400' or 6300' (Sweden).
Often both 360o and 6400' are used, i.e. double graduation.

That's all I've managed to find.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Definitions
High School Euclidean/Plane Geometry
High School Geometry
Middle School Definitions
Middle School Geometry
Middle School Terms/Units of Measurement
Middle School Two-Dimensional Geometry

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