Coordinate Systems Overview
Peter H. Dana
These materials were developed by Peter H. Dana, Department of
Geography, University of Texas at Austin, 1995. These
be used for study, research, and education in not-for-profit
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H. Dana, The Geographer's Craft Project, Department of
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Table of Contents is provided.
Revised: 12/15/99 (Orignally published in July, 1995)
This overview of coordinate systems for georeferencing provides
description of local and global systems for use in precise
navigation, and geographic information systems for the location
There are many different coordinate systems, based on a variety
datums, units, projections, and reference systems in use today.
As an example, this overview often uses the position of one of
of geodetic control points in the United States, the star in the
the Goddess of Liberty atop the Capitol building in Austin,
Basic Coordinate Systems
There are many basic coordinate systems familiar to students of
These systems can represent points in two-dimensional or
René Descartes (1596-1650) introduced systems of coordinates
on orthogonal (right angle) coordinates.
These two and three-dimensional systems used in analytic
geometry are often
referred to as Cartesian systems.
Similar systems based on angles from baselines are often
referred to as
Plane Coordinate Systems
Two-dimensional coordinate systems are defined
to a single plane.
Ellipsoidal earth models are required for accurate range and
over long distances. Loran-C, and GPS navigation receivers use
earth models to compute position and waypoint information.
models define an ellipsoid with an equatorial radius and a polar
The best of these models can represent the shape of the earth
smoothed, averaged sea-surface to within about one-hundred
Reference ellipsoids are defined by semi-major (equatorial
semi-minor (polar radius) axes.
Other reference ellipsoid parameters such as flattening, and
are computed from these two terms.
Many reference ellipsoids are in use by different nations and
Geodetic datums define the reference systems that describe the
shape of the earth. Hundreds of different datums have been used
position descriptions since the first estimates of the earth's
made by Aristotle. Datums have evolved from those describing a
earth to ellipsoidal models derived from years of satellite
Modern geodetic datums range from flat-earth models used for
to complex models used for international applications which
describe the size, shape, orientation, gravity field, and
of the earth. While cartography, surveying, navigation, and
make use of geodetic datums, the science of geodesy is the
for the topic.
Referencing geodetic coordinates to the wrong datum can result
errors of hundreds of meters. Different nations and agencies use
datums as the basis for coordinate systems used to identify
geographic information systems, precise positioning systems, and
systems. The diversity of datums in use today and the
that have made possible global positioning measurements with
accuracies requires careful datum selection and careful
coordinates in different datums.
Overview, Department of Geography, University of Texas at
Latitude, Longitude, Height
The most commonly used coordinate system today is the
and height system.
The Prime Meridian and the Equator are the reference planes
used to define
latitude and longitude.
and Prime Meridian
The geodetic latitude (there are many other defined latitudes)
of a point
is the angle from the equatorial plane to the vertical
direction of a line
normal to the reference ellipsoid.
The geodetic longitude of a point is the angle between a
and a plane passing through the point, both planes being
to the equatorial plane.
The geodetic height at a point is the distance from the
to the point in a direction normal to the ellipsoid.
Latitude, Longitude, and Height
ECEF X, Y, Z
Earth Centered, Earth Fixed Cartesian coordinates are also
used to define
three dimensional positions.
Earth centered, earth-fixed, X, Y, and Z, Cartesian
coordinates (XYZ) define
three dimensional positions with respect to the center of mass
of the reference
The Z-axis points toward the North Pole.
The X-axis is defined by the intersection of the plane define
by the prime
meridian and the equatorial plane.
The Y-axis completes a right handed orthogonal system by a
plane 90 degrees
east of the X-axis and its intersection with the equator.
X, Y, and Z
X, Y, Z Coordinate Example
Universal Transverse Mercator
Universal Transverse Mercator (UTM) coordinates define two
UTM zone numbers designate 6 degree longitudinal strips
80 degrees South latitude to 84 degrees North latitude.
UTM zone characters designate 8 degree zones extending north
from the equator.
There are special UTM zones between 0 degrees and 36 degrees
above 72 degrees latitude and a special zone 32 between 56
64 degrees north latitude.
Each zone has a central meridian. Zone 14, for example, has a
of 99 degrees west longitude. The zone extends from 96 to 102
Eastings are measured from the central meridian (with a 500km
to insure positive coordinates).
Northings are measured from the equator (with a 10,000km false
for positions south of the equator).
Zone 14 Example Detail
Military Grid Reference
The Military Grid Reference System (MGRS) is an extension of
the UTM system.
UTM zone number and zone character are used to identify an
area 6 degrees
in east-west extent and 8 degrees in north-south extent.
UTM zone number and designator are followed by 100 km square
The system uses a set of alphabetic characters for the 100 km
Starting at the 180 degree meridian the characters A to Z
(omitting I and
O) are used for 18 degrees before starting over.
From the equator north the characters A to V (omitting I and
O) are used
for 100 km squares, repeating every 2,000 km.
Northing designators normally begin with 'A' at the equator
for odd numbered
UTM easting zones.
For even numbered easting zones the northing designators are
five characters, starting at the equator with 'F'.
South of the equator, the characters continue the pattern
set north of
Complicating the system, ellipsoid junctions (spheroid
junctions in the
terminology of MGRS) require a shift of 10 characters in the
km grid square designators. Different geodetic datums using
ellipsoids use different starting row offset numbers to
Grid Reference System
UTM zone number, UTM zone, and the two 100 km square
characters are followed
by an even number of numeric characters representing easting
If 10 numeric characters are used, a precision of 1 meter is
2 characters imply a precision of 10 km.
From 2 to 10 numeric characters the precision changes from
10 km, 1 km,
100 m 10 m, to 1 m.
World Geographic Reference
The World Geographic Reference System is used for aircraft
GEOREF is based on latitude and longitude.
The globe is divided into twelve bands of latitude and
of longitude, each 15 degrees in extent.
Geographic Reference System Index
These 15 degree areas are further divided into one degree
by 15 characters.
1 Degree Grid
Two numeric characters designate the integer number of minutes
east of the one degree quadrangle boundary longitude.
Two additional numeric characters designate the number of
minutes of latitude
north of the one degree quadrangle boundary latitude.
The World Geographic Reference System can be extended to refer
areas of operation.
A larger East-West area can be designated by adding an "S" and
of of nautical miles to the east and west sides of the
A larger north-south area can be designated by adding an "X"
and the number
of nautical miles to the north and south.
A circular area can be designated by adding an "R" and the
radius of the
circle in nautical miles.
An altitude zone can be defined by adding an "H" and a value
The number of digits indicates the precision of the value.
implies units in feet. Four digits implies tens of feet, three
hundreds of feet, and two digits, thousands of feet.
National Grid Systems
Many nations have defined grid systems based on coordinates
their territory. Australia, Belgium, Great Britain, Finland
, Ireland, Italy, The Netherlands, New Zealand, and Sweden are
of nations that have defined a National Grid System.
British National Grid (BNG)
The British National Grid (BNG) is based on the National
Grid System of
England, administered by the British Ordnance Survey.
The BNG has been based on a Transverse Mercator projection
since the 1920s.
The modern BNG is based on the Ordnance Survey of Great
Britain Datum 1936
The true origin of the system is at 49 degrees north
latitude and 2 degrees
The false origin is 400 km west and 100 km north.
Scale at the central meridian is 0.9996012717
The first BNG designator defines a 500 km square.
The second designator defines a 100 km square.
Grid 100 km Squares
The remaining numeric characters define 10 km, 1 km, 100 m,
10 m, or 1
m eastings and northings.
National Grid Example
Irish National Grid
The Irish National Grid (ING) is administered by the Irish
The ING has been based on a Transverse Mercator projection
since the 1920s.
The ING is based on the Ordnance Survey of Great Britain Datum
the Ireland Datum 1965.
The true origin of the system is at 53 degrees, 30 minutes
and 8 degrees west longitude.
The false origin is 200 km west and 250 km south of the true
Scale at the central meridian is 1.000035.
The first ING designator defines a 100 km square.
National Grid 100 km Squares
The remaining numeric characters define 10 km, 1 km, 100 m, 10
m, or 1
m eastings and northings.
National Grid Example
State Plane Coordinates
In the United States, the State Plane System was developed in
and was based on the North American Datum 1927 (NAD27).
The State Plane System 1983 is based on the North American
Datum 1983 (NAD83).
NAD 83 coordinates are based on the meter.
State plane systems were developed in order to provide local
systems that were tied to a national datum.
Some smaller states use a single state plane zone.
Larger states are divided into several zones.
State plane zone boundaries often follow county boundaries.
Lambert Conformal Conic projections are used for rectangular
a larger east-west than north- south extent.
Transverse Mercator projections are used to define zones with
One State Plane zone in Alaska uses an oblique Mercator
a thin diagonal area.
Public Land Rectangular
Public Land Rectangular Surveys have been used since the 1790s
public lands in the United States.
The system is based on principal meridians and baselines.
Townships, approximately six miles square, are numbered with
to baseline and principal meridian.
Ranges are the distances and directions from baseline and
in numbers of townships.
Every four townships a new baseline is established so that
can remain north oriented.
Sections, approximately one mile square, are numbered from 1
to 36 within
Sections are divided into quarter sections.
Quarter sections are divided into 40-acre, quarter-quarter
Quarter-quarter sections are sometimes divided into 10-acre
Fractional units of section quarters, designated as numbered
result from irregular claim boundaries, rivers, lakes, etc.
Abbreviations are used for Township (T or Tps), Ranges (R or
or secs), and directions (N, E, S, W, NE, etc.).
Township and Range Property Description
Metes and Bounds
Metes and Bounds identify the boundaries of land parcels by
lengths and directions of lines.
Lines are described with respect to natural or artificial
baselines defined by these monuments.
The metes and bounds survey is based on a point of beginning,
Line lengths are measured along a horizontal level plane.
Directions are bearing angles measured with respect to a
in the survey.
and Bounds Example
Postal codes such as the United States ZIP code can be used to
Three digit codes identify large areas.
Maidenhead Grid Squares
The Maidenhead Grid Square system was designed to facilitate
of geographical positions for use within the amateur radio
Maidenhead Grid identifies "Fields" consisting of an area
of longitude by ten degrees of latitude with two alphabetic
An additional set of two numeric digits locates a specific
of longitude by one-degree of latitude" grid square" area
within the Field.
Two additional alphabetic characters can be used to refer to a
of longitude by 2.5 minutes of latitude "Sub-Square" within
the Grid Square.
In each case the longitude character precedes the latitude
Variations and extensions to the Maidenhead system are in
use. Some Global
Positioning System (GPS) receivers display positions in an
system that appends one or two additional sets of numeric
pairs, increasing the precision with which a location can be
Some amateur radio operators use other terms for the
such as World Wide Locator (WWL) squares or QTH locator
Ham operators use these grid designators to communicate
to each other. Several utility programs are available to
latitude and longitude and the Maidenhead Grid Square
system. Some of these
also allow computation of distance and azimuth between
Grid Square Fields
AT&T V and H
The AT&T V and H (Vertical and Horizontal) coordinate
system was devised
in 1957 by Jay K. Donald for the easy computation of distances
telephone switching centers. The system is based on the Donald
Projection, a two-point equidistant projection covering the
of the continental United States and Canada. The system is
based on units
of the square-root of one-tenth of a mile.
Once the coordinates of switching sites are known, distances
can be simply found by calculating the square root of the sum
of the squares
of the differences in the vertical and horizontal coordinates
ten. Designed for simple distance calculations that could be
in the field with a slide rule, the system is still found
imbedded in some
telephone rate computation software.
Navigation systems can define locations by referencing
Loran-C time-differences can identify positions with an
accuracy of one-quarter
of a mile.
Omega phase-differences can identify positions with an
accuracy of 1-5
VOR-DME (Very high frequency Omni Range - Distance
from an aircraft can identify locations with an accuracy of
Navigational buoys, and other aids to navigation can be used
reference points, bearings to visual references can identify
with varying accuracies.
Defense Mapping Agency. 1977. The American Practical Navigator
No. 9, Defense Mapping Agency Hydrographic Center.
Laurila, Simo H. 1976. Electronic Surveying and Navigation.
New York: John
Wiley & Sons
Muehrcke, P.C and Juliana O. Muehrcke. 1992. Map Use. Madison,
WI: JP Publications.
National Imagery and Mapping Agency. 1997. World Geodetic
System 1984 (WGS
84) - Its Definition and Relationships with Local Geodetic
Edition. Washington, DC: National Imagery and Mapping Agency.
Snyder, John P. 1987. Map Projections, A Working Manual.
US Govt. Printing Office.
Thomas, P. D. 1970. Spheroidal Geodesics, Reference Systems
and Local Geometry.
Washington, DC: U. S. Naval Oceanographic Office.
U. S. Air Force and Navy. 1983. Air Navigation, AFM 51-40.
DC: Department of the Air Force.
U. S. Army. 1967. TM 5-241-1 Grids and Grid References.
Department of the Army.