# Special Coordinate Systems

This section helps you become familiar with the coordinate systems that are supported in the Geographic Calculator. You also can define your own additional custom coordinate systems.

More:

Geodetic

Universal Transverse Mercator

State Plane

XYZ Cartesian Earth Centered Earth Fixed

The New Zealand Map Grid

Military Grid Reference System (MGRS)

World_Geographic_Reference_System

ATS (Alberta Township System)

# Geodetic

A Geodetic Coordinate System is a three-dimensional coordinate system defined by an ellipsoid, the equatorial plane of the ellipsoidal and a plane defined along the polar axis (a meridional plane).

Coordinates in a Geodetic Coordinate System are given by a geodetic latitude (the angle between the normal to the ellipsoid at a location and the equatorial plane), a geodetic longitude (the angle between the meridional reference plane and a meridional plane containing the normal to the ellipsoid at a location) and a geodetic height (the perpendicular distance of a location from the ellipsoid).

A geodetic datum is the only required defining parameter for a Geodetic Coordinate System in the Geographic Calculator. A geodetic datum defines constants that relate a Geodetic Coordinate System to the physical earth, the dimensions of the reference ellipsoid, the location of the origin of the system, and the orientation of the system.

A geodetic coordinate is specified in the Geographic Calculator by latitude, longitude, and ellipsoidal height values. Any angular unit defined within the Geographic Calculator may be used to specify latitude and longitude coordinates.

The ellipsoidal height of a location is defined as the elevation of the location above the geoid (essentially a modeled surface representing mean sea level) and the separation of the geoid surface from the ellipsoidal surface. The Geographic Calculator assumes a value of 0.0 if the ellipsoidal height of a location is unknown. Any distance unit defined within the Geographic Calculator may be used to specify ellipsoidal height values.

# Universal Transverse Mercator

The Universal Transverse Mercator (UTM) Coordinate System is an international plane coordinate system developed by the U.S. Army. It extends around the globe from 84 degrees north to 80 degrees south. The world is divided into 60 zones in the Northern Hemisphere and 60 corresponding zones in the southern hemisphere. Each zone covers 6 degrees of longitude. Each zone extends 3 degrees eastward and 3 degrees westward from its central meridian. Zones are numbered west to east from the 180-degree meridian.

The geodetic datum and the UTM zone are required parameters for the UTM Coordinate System supported in the Geographic Calculator.

A UTM coordinate is specified in the Geographic Calculator by northing and easting values. The meter is the standard unit in the UTM Coordinate System. Any distance unit defined within the Geographic Calculator may be used to specify UTM coordinates.

# US State Plane

There are two State Plane Coordinate Systems defined in the United States, one based on the North American Datum of 1927 and the other based on the North American Datum of 1983.

Each of the State Plane Coordinate Systems divides the United States into over 130 sections, each with its own projection surface and grid network. With the exception of very narrow states, such as Delaware, New Jersey, and New Hampshire, most states divide into two to ten zones.

Zones extending primarily in an east-west direction are based on the Lambert Conformal Projection, while zones extending in a north-south direction are based on the Transverse Mercator Projection. Alaska, Florida and New York use both Transverse Mercator and Lambert Conformal for different areas. The Aleutian panhandle of Alaska uses the Oblique Mercator Projection.

Zone boundaries follow state and county lines and, because each zone is small, distortion is less than 1 in 10,000. Each zone has a centrally located origin and a central meridian that passes through the origin. The United States uses a two-zone numbering system: The United States Geological Survey (USGS) Code System and the National Ocean Service (NOS) Code System. However, other code systems do exist.

The State Plane zone is the only required defining parameter for any of the State Plane Coordinate Systems supported in the Geographic Calculator.

WE STRONGLY RECOMMEND THAT YOU USE THE NGS NADCON GEODETIC DATUM TRANSFORMATION METHOD WHEN CONVERTING STATE PLANE COORDINATES. HOWEVER, YOU MAY USE THE MOLODENSKY METHOD WHEN CONVERTING STATE PLANE COORDINATE SYSTEM OF 1927 COORDINATES AND SELECT ONE OF THE DEFINED SET OF NAD 27 DATUM TRANSFORMATIONS.

A State Plane coordinate is specified in the Geographic Calculator by northing and easting values. The U.S. Survey Foot is the standard unit in the State Plane Coordinate System of 1927. The meter is the standard unit in the State Plane Coordinate System of 1983. Any distance unit defined within the Geographic Calculator may be used to specify State Plane coordinates.

State Plane 1927 and State Plane 1927 Exact

# Geocentric - XYZ Cartesian Earth Centered Earth Fixed

An XYZ Cartesian Earth Centered Earth Fixed (ECEF) Coordinate System is a coordinate system with the origin at the center of the earth (as defined by a reference ellipsoid). The Z-axis coincides with the minor axis of the reference ellipsoid. The X-axis runs from the origin through a point on the equatorial plane at the zero meridian. The Y-axis is perpendicular to the X-axis on the equatorial plane.

A geodetic datum is the only required defining parameter for an XYZ Cartesian ECEF Coordinate System in the Geographic Calculator. A geodetic datum defines constants that relate a Geodetic Coordinate System to the physical earth, to the dimensions of the reference ellipsoid, to the location of the origin of the system and to the orientation of the system.

An XYZ Cartesian ECEF coordinate is specified in the Geographic Calculator by X, Y, and Z values in any of the defined distance units of measure.

# The New Zealand Map Grid

The North Island and South Island of New Zealand have been mapped on one projection with one grid known as the New Zealand Map Grid.

The projection adopted was derived from mathematical analysis to give a small range of scale variation over the land area of New Zealand. This has been achieved at the expense of abandoning the orderly arrangement of scale curves. Such a projection has no recognized name. It is simply called the New Zealand Map Grid projection. The projection is conformal but is unlike any other projection used for detailed mapping.

Easting values are always less than 5,000,000 meters and northing values are always greater than 5,000,000 meters.

There are no required parameters for defining a New Zealand Map Grid Coordinate System in the Geographic Calculator.

# The Military Grid Reference System (MGRS)

The Military Grid Reference System (MGRS) is a two-dimensional grid that uniquely identifies a square meter anywhere on the earth. The MGRS attempts to represent the entire surface of the Earth on a worldwide grid. The grid is based on the UTM (between 80°S and 84°N latitudes) and UPS (Universal Polar Stereographic) systems.

Currently, the Geographic Calculator only supports MGRS points in the UTM-based latitude range (between 80°S and 84°N ).

MGRS coordinates are comprised of 7 parts, 3 of which correspond to the UTM/UPS zone that contains the coordinate. In addition to the Datum (which is not explicitly expressed in the MGRS coordinate), the UTM/UPS zone and latitude band (described below) are part of the MGRS point.

UTM

• The UTM area is divided into 60 longitudinal strips, each 6° wide. The strips are numbered 1-60 beginning at the 180°-174° W (Zone 1) and increase to the East (i.e. 174°-168° W = Zone 2, etc.).

• Each strip (i.e. Zone) is then divided (horizontally) into 8° latitude bands. The bands are lettered “C” (80° S) through “X” (80° N) omitting the letters “I” and “O”.

More on MGRS Coordinates

See example MGRS grid

World Geographic Reference System (WGRS)

The World Geographic Reference system (WGRS) is based on geodetic latitude and longitude coordinates, and uses an alpha-numeric string to represent points on the grid in the following display format:

AAAANNNNNNNNNN

Where N represents a numeral and A represents a letter. The first two letters denote the major grid division, which corresponds to a unique 15-degree quadrangle on the surface of the earth. The first letter, representing the division’s longitudinal location, ranges from A to Z. The second letter, representing the division’s latitudinal location, ranges from A to M. Both ranges exclude letters O and I.

The second two letters denote the minor grid division, which identifies a 1-degree quadrangle within the major division’s quadrangle. The first letter represents longitudinal location and the second the latitudinal location. Both letters range from A to Q, excluding O and I.

The ten numerals represent two offset values, in decimal minutes, within the minor division's quadrangle from the quadrangle’s southwest corner. The first five numerals represent the easting offset and the second five represent the northing offset.  There are two values to represent minutes from the quadrangle corner, and three values to represent fractions of minutes.  *Note:  values in the negative direction (West and South values) will appear as a difference from the corner.  In the case of a coordinate such as W 122 15 00 ,  N 45 40 000 the value will appear as: DKNA4500040000

PRECISION NOTE: WGRS coordinates are only accurate to within 0.75 meters, due to the rigid formatting of the strings and the precision used by the format.  Converting to WGRS from other coordinates that use higher precision can cause a loss of data accuracy.