Coordinate Systems Overview
Peter H. Dana
These materials may be used for study, research, and education in notforprofit
applications. All commercial rights are reserved. Please credit the author,
Peter H. Dana, The Geographer's Craft Project, Department of Geography,
The University of Colorado at Boulder. Copyright © 1999 Peter H. Dana.
This page is available in a framed
version. For convenience, a Full
Table of Contents is provided.
Revised: 12/15/99 (Orignally published in July, 1995)
Associated Overviews
Introduction

This overview of coordinate systems for georeferencing provides a brief
description of local and global systems for use in precise positioning,
navigation, and geographic information systems for the location of points
in space.

There are many different coordinate systems, based on a variety of geodetic
datums, units, projections, and reference systems in use today.

As an example, this overview often uses the position of one of the thousands
of geodetic control points in the United States, the star in the hand of
the Goddess of Liberty atop the Capitol building in Austin, Texas.
Table
of Contents
Basic Coordinate Systems

There are many basic coordinate systems familiar to students of geometry
and trigonometry.

These systems can represent points in twodimensional or threedimensional
space.

René Descartes (15961650) introduced systems of coordinates based
on orthogonal (right angle) coordinates.

These two and threedimensional systems used in analytic geometry are often
referred to as Cartesian systems.

Similar systems based on angles from baselines are often referred to as
polar systems.

Plane Coordinate Systems

Twodimensional coordinate systems are defined with respect
to a single plane.

ThreeDimensional Systems

Table
of Contents
Reference Ellipsoids

Ellipsoidal earth models are required for accurate range and bearing calculations
over long distances. LoranC, and GPS navigation receivers use ellipsoidal
earth models to compute position and waypoint information. Ellipsoidal
models define an ellipsoid with an equatorial radius and a polar radius.
The best of these models can represent the shape of the earth over the
smoothed, averaged seasurface to within about onehundred meters.

Reference ellipsoids are defined by semimajor (equatorial radius) and
semiminor (polar radius) axes.

Other reference ellipsoid parameters such as flattening, and eccentricity
are computed from these two terms.

Reference
Ellipsoid Parameters

Many reference ellipsoids are in use by different nations and agencies.

Selected
Reference Ellipsoids

Table
of Contents
Geodetic Datums

Geodetic datums define the reference systems that describe the size and
shape of the earth. Hundreds of different datums have been used to frame
position descriptions since the first estimates of the earth's size were
made by Aristotle. Datums have evolved from those describing a spherical
earth to ellipsoidal models derived from years of satellite measurements.

Modern geodetic datums range from flatearth models used for plane surveying
to complex models used for international applications which completely
describe the size, shape, orientation, gravity field, and angular velocity
of the earth. While cartography, surveying, navigation, and astronomy all
make use of geodetic datums, the science of geodesy is the central discipline
for the topic.

Referencing geodetic coordinates to the wrong datum can result in position
errors of hundreds of meters. Different nations and agencies use different
datums as the basis for coordinate systems used to identify positions in
geographic information systems, precise positioning systems, and navigation
systems. The diversity of datums in use today and the technological advancements
that have made possible global positioning measurements with submeter
accuracies requires careful datum selection and careful conversion between
coordinates in different datums.

Geodetic
Datum Overview, Department of Geography, University of Texas at Austin

Table
of Contents
Coordinate Systems
Global Systems

Latitude, Longitude, Height

The most commonly used coordinate system today is the latitude, longitude,
and height system.

The Prime Meridian and the Equator are the reference planes used to define
latitude and longitude.

Equator
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 reference plane
and a plane passing through the point, both planes being perpendicular
to the equatorial plane.

The geodetic height at a point is the distance from the reference ellipsoid
to the point in a direction normal to the ellipsoid.

Geodetic
Latitude, Longitude, and Height

Table
of Contents

ECEF X, Y, Z

Earth Centered, Earth Fixed Cartesian coordinates are also used to define
three dimensional positions.

Earth centered, earthfixed, X, Y, and Z, Cartesian coordinates (XYZ) define
three dimensional positions with respect to the center of mass of the reference
ellipsoid.

The Zaxis points toward the North Pole.

The Xaxis is defined by the intersection of the plane define by the prime
meridian and the equatorial plane.

The Yaxis completes a right handed orthogonal system by a plane 90 degrees
east of the Xaxis and its intersection with the equator.

ECEF
X, Y, and Z

ECEF
X, Y, Z Coordinate Example

Table
of Contents

Universal Transverse Mercator (UTM)

Universal Transverse Mercator (UTM) coordinates define two dimensional,
horizontal, positions.

UTM zone numbers designate 6 degree longitudinal strips extending from
80 degrees South latitude to 84 degrees North latitude.

UTM zone characters designate 8 degree zones extending north and south
from the equator.

There are special UTM zones between 0 degrees and 36 degrees longitude
above 72 degrees latitude and a special zone 32 between 56 degrees and
64 degrees north latitude.

UTM
Zones

Each zone has a central meridian. Zone 14, for example, has a central meridian
of 99 degrees west longitude. The zone extends from 96 to 102 degrees west
longitude.

UTM
Zone 14

Eastings are measured from the central meridian (with a 500km false easting
to insure positive coordinates).

Northings are measured from the equator (with a 10,000km false northing
for positions south of the equator).

UTM
Zone 14 Example Detail

UTM
Coordinate Example

Table
of Contents

Military Grid Reference System (MGRS)

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 eastwest extent and 8 degrees in northsouth extent.

UTM zone number and designator are followed by 100 km square easting and
northing identifiers.

The system uses a set of alphabetic characters for the 100 km grid squares.

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 offset by
five characters, starting at the equator with 'F'.

South of the equator, the characters continue the pattern set north of
the equator.

Complicating the system, ellipsoid junctions (spheroid junctions in the
terminology of MGRS) require a shift of 10 characters in the northing 100
km grid square designators. Different geodetic datums using different reference
ellipsoids use different starting row offset numbers to accomplish this.

Military
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 and northing
values.

If 10 numeric characters are used, a precision of 1 meter is assumed.

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.

Table
of Contents

World Geographic Reference System (GEOREF)

The World Geographic Reference System is used for aircraft navigation.

GEOREF is based on latitude and longitude.

The globe is divided into twelve bands of latitude and twentyfour zones
of longitude, each 15 degrees in extent.

World
Geographic Reference System Index

These 15 degree areas are further divided into one degree units identified
by 15 characters.

GEOREF
1 Degree Grid

Two numeric characters designate the integer number of minutes of longitude
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.

GEOREF
Example

The World Geographic Reference System can be extended to refer to larger
areas of operation.

A larger EastWest area can be designated by adding an "S" and the number
of of nautical miles to the east and west sides of the referenced point.

A larger northsouth 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 of altitude.
The number of digits indicates the precision of the value. Five digits
implies units in feet. Four digits implies tens of feet, three digits,
hundreds of feet, and two digits, thousands of feet.

Table
of Contents

National Grid Systems

Many nations have defined grid systems based on coordinates that cover
their territory. Australia, Belgium, Great Britain, Finland
, Ireland, Italy, The Netherlands, New Zealand, and Sweden are a examples
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
(Airy Ellipsoid).

The true origin of the system is at 49 degrees north latitude and 2 degrees
west longitude.

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.

British
National Grid 100 km Squares

The remaining numeric characters define 10 km, 1 km, 100 m, 10 m, or 1
m eastings and northings.

British
National Grid Example

Table
of Contents

Irish National Grid

The Irish National Grid (ING) is administered by the Irish Ordnance Survey.

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 1936 or
the Ireland Datum 1965.

The true origin of the system is at 53 degrees, 30 minutes north latitude
and 8 degrees west longitude.

The false origin is 200 km west and 250 km south of the true origin.

Scale at the central meridian is 1.000035.

The first ING designator defines a 100 km square.

Irish
National Grid 100 km Squares

The remaining numeric characters define 10 km, 1 km, 100 m, 10 m, or 1
m eastings and northings.

Irish
National Grid Example

Table
of Contents

State Plane Coordinates

In the United States, the State Plane System was developed in the 1930s
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 reference
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 zones with
a larger eastwest than north south extent.

Transverse Mercator projections are used to define zones with a larger
northsouth extent.

One State Plane zone in Alaska uses an oblique Mercator projection for
a thin diagonal area.

Table
of Contents

Public Land Rectangular Surveys

Public Land Rectangular Surveys have been used since the 1790s to identify
public lands in the United States.

The system is based on principal meridians and baselines.

Townships, approximately six miles square, are numbered with reference
to baseline and principal meridian.

Ranges are the distances and directions from baseline and meridian expressed
in numbers of townships.

Every four townships a new baseline is established so that orthogonal meridians
can remain north oriented.

U.S.
Rectangular Survey

Sections, approximately one mile square, are numbered from 1 to 36 within
a township.

Township
Sections

Sections are divided into quarter sections.

Quarter sections are divided into 40acre, quarterquarter sections.

Quarterquarter sections are sometimes divided into 10acre areas.

Subdivided
Section

Fractional units of section quarters, designated as numbered lots, often
result from irregular claim boundaries, rivers, lakes, etc.

Abbreviations are used for Township (T or Tps), Ranges (R or Rs), Sections(sec
or secs), and directions (N, E, S, W, NE, etc.).

A
Township and Range Property Description

Table
of Contents

Metes and Bounds

Metes and Bounds identify the boundaries of land parcels by describing
lengths and directions of lines.

Lines are described with respect to natural or artificial monuments and
baselines defined by these monuments.

The metes and bounds survey is based on a point of beginning, an established
monument.

Line lengths are measured along a horizontal level plane.

Directions are bearing angles measured with respect to a previous line
in the survey.

Metes
and Bounds Example

Table
of Contents

Miscellaneous Systems

Postal Codes

Postal codes such as the United States ZIP code can be used to identify
areas.

Three digit codes identify large areas.

Maidenhead Grid Squares

The Maidenhead Grid Square system was designed to facilitate the designation
of geographical positions for use within the amateur radio community. The
Maidenhead Grid identifies "Fields" consisting of an area twenty degrees
of longitude by ten degrees of latitude with two alphabetic characters.
An additional set of two numeric digits locates a specific twodegrees
of longitude by onedegree of latitude" grid square" area within the Field.
Two additional alphabetic characters can be used to refer to a 5.0 minutes
of longitude by 2.5 minutes of latitude "SubSquare" within the Grid Square.
In each case the longitude character precedes the latitude designator.

Variations and extensions to the Maidenhead system are in use. Some Global
Positioning System (GPS) receivers display positions in an extended Maidenhead
system that appends one or two additional sets of numeric and alphabetic
pairs, increasing the precision with which a location can be specified.

Some amateur radio operators use other terms for the Maidenhead system
such as World Wide Locator (WWL) squares or QTH locator squares.

Ham operators use these grid designators to communicate transmitter positions
to each other. Several utility programs are available to convert between
latitude and longitude and the Maidenhead Grid Square system. Some of these
also allow computation of distance and azimuth between stations.

Maidenhead
Grid Square Fields

Maidenhead
Grid Squares

Maidenhead
Grid SubSquares

AT&T V and H Coordinate System

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 between
telephone switching centers. The system is based on the Donald Elliptic
Projection, a twopoint equidistant projection covering the land masses
of the continental United States and Canada. The system is based on units
of the squareroot of onetenth of a mile.

Once the coordinates of switching sites are known, distances between sites
can be simply found by calculating the square root of the sum of the squares
of the differences in the vertical and horizontal coordinates divided by
ten. Designed for simple distance calculations that could be accomplished
in the field with a slide rule, the system is still found imbedded in some
telephone rate computation software.

Navigation System Coordinates

Navigation systems can define locations by referencing measurements of
electronic signals.

LoranC timedifferences can identify positions with an accuracy of onequarter
of a mile.

Omega phasedifferences can identify positions with an accuracy of 15
kms.

VORDME (Very high frequency Omni Range  Distance Measuring) measurements
from an aircraft can identify locations with an accuracy of 0.53 kms.

Navigational buoys, and other aids to navigation can be used as visual
reference points, bearings to visual references can identify locations
with varying accuracies.

Navigational
Buoy

Table
of Contents

References

Defense Mapping Agency. 1977. The American Practical Navigator Publication
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 Systems, 3rd
Edition. Washington, DC: National Imagery and Mapping Agency.

Snyder, John P. 1987. Map Projections, A Working Manual. Washington, DC:
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 5140. Washington,
DC: Department of the Air Force.

U. S. Army. 1967. TM 52411 Grids and Grid References. Washington, DC:
Department of the Army.
Table
of Contents