# UNCLASSIFIED

Description of Geocentric Coordinates

Geocentric coordinates are three-dimensional Cartesian coordinates (X, Y, Z) that define the position of a point with respect to the center of mass of the earth. The origin of the coordinate system is at the center of the reference ellipsoid. The coordinate system is a right-handed system, with the positive X axis emerging from the ellipsoid at the equator on the prime meridian, and the positive Z axis emerging from the ellipsoid at the north pole.

Description of Local Cartesian Coordinates

A local Cartesian coordinate system is primarily defined by the location of its origin, in geodetic coordinates. If the specified origin height is zero, the local XY plane is tangent to the surface of the reference ellipsoid at the specified origin. If the origin height is non-zero, the local XY plane is shifted up or down accordingly. If the specified orientation angle is zero, the local positive Y axis points north, while the local positive X axis points east, and the local positive Z axis points "up", perpendicular to the ellipsoid surface at the origin. If the orientation angle is not zero, then the local Cartesian coordinate system is rotated clockwise about the Z axis by the specified amount. For example, if the orientation angle is 90°, the local positive Y axis will point east, while the local positive X axis points south.

Description of Geodetic Coordinates

Geodetic coordinates consist of geodetic latitude (f), geodetic longitude (l), and geodetic height (h) which define the position of a point on, or near, the surface of the earth with respect to a reference ellipsoid. Their relationship to the reference ellipsoid is shown in the figure below. The angle between the normal SP and the equatorial (X-Y) plane is called the geodetic latitude (f) of point P. The meridian plane containing point P is defined as the half-plane containing the Z-axis and point P. The angle between the prime meridian (X-Z) plane and the meridian containing point P is the geodetic longitude (l) of point P. Geodetic longitude is not defined when P lies on the Z-axis. The distance from Q to P is called the geodetic or ellipsoidal height (h).

Relationship Between Geocentric and Geodetic Coordinates

Latitude limits:

-90° (90°S) to +90° (90°N )

Longitude limits:

0° to 360° or -180° (180°W) to +180° (180°E)

Description of GEOREF Coordinates

The World Geographic Reference System (GEOREF) is an alpha-numeric system for reporting positions for air defense and strategic air operations. It is based on geodetic coordinates. The first two letters in a GEOREF coordinate string identify a 15° quadrangle, as shown below. The next two letters define a 1° cell within that quadrangle, also as shown below. The remaining digits define the location within the cell in terms of decimal minutes of longitude and latitude, with a maximum resolution of 0.001 minutes (approximately 2 meters).

GEOREF 15° Quadrangles

GEOREF 1° Cells within a 15° Quadrangle

Description of GARS Coordinates

The Global Area Reference System (GARS) is an alpha-numeric system which divides the world into 30 minute cells using quadrant/keypad tiling. The first three numbers identify the 30 minute east/west quadrangle, ranging from 1 to 720. The next two letters identify the 30 minute north/south quadrangle, ranging from AA to QZ, omitting I and O. The next number identifies a 15 minute cell within that quadrangle. This value ranges from 1 to 4, arranged left to right, top to bottom. The last number identifies a 5 minute cell within the 15 minute cell. This value ranges from 1 to 9, arranged as a keypad left to right, top to bottom.

GARS Quadrant/Keypad Tiling

Description of MGRS Coordinates

The Military Grid Reference System (MGRS) is an alpha-numeric system, based upon the UTM and UPS map projections, for identifying positions. An MGRS coordinate consists of a zone designation, alphabetic 100,000-meter grid square designator, and numeric coordinates within the 100,000 meter grid square. MGRS coordinates are defined for the primary UTM and UPS areas, but not for the overlap areas along the polar region boundaries.

In the UTM area, MGRS coordinates are based on the ellipsoid, geodetic latitude, UTM zone, Easting and Northing as follows:

a. The first two characters of the MGRS coordinate are the two digits of the numeric UTM zone. Leading zeros must be included. The figure below shows the layout of the zones, including the irregular zones in the North Atlantic.

b. The third character of the MGRS coordinate is a letter representing a band of geodetic latitude. Beginning at 80°S and proceeding northward, the 20 bands are lettered C through X, omitting I and O. The bands are all 8° high except band X (72°N to 84°N), which is 12° high. The figure below shows the layout of these bands.

MGRS Zones and Bands

c. The fourth and fifth characters of the MGRS coordinate are a pair of letters representing the 100,000-meter grid square. Two different patterns of two-letter designations are used, depending on the ellipsoid associated with the current datum. The first diagram below shows the pattern of 100,000 meter square designations used with the Clarke 1866, Clarke 1880, Bessel 1841 and Bessel 1841 Namibia ellipsoids. The second diagram shows the pattern used with all other ellipsoids. The patterns are repeated every six zones.

Note: The alphabetic method of designating 100,000-meter grid squares has changed over time. Older products may have different grid square designations.

MGRS 100,000m Square Designations (AL Pattern)

MGRS 100,000m Square Designations (AA Pattern)

d. The remainder of the MGRS coordinate string consists of the numeric Easting and Northing values within the 100,000-meter grid square. The left half of the digit sequence is the Easting value, which is read to the right from the left edge of the 100,000-meter grid square. The right half of the digit sequence is the Northing value, which is read northward from the bottom edge of the 100,000-meter grid square. Both the Easting and Northing values are within the range from 0 to 100,000 meters. Both Easting and Northing values must have the same resolution and must include leading zeros.

In the UPS area, MGRS coordinates are based on the ellipsoid, geodetic latitude and longitude, Easting, and Northing as follows:

a. The first character of the MGRS coordinate is:

A in the Southern and Western Hemispheres,

B in the Southern and Eastern Hemispheres,

Y in the Northern and Western Hemispheres, and

Z in the Northern and Eastern Hemispheres.

b. The second and third characters of the MGRS coordinate are letters representing a 100,000 meter grid square. The diagrams below show the layout of the 100,000 meter squares in the north and south polar zones.

MGRS 100,000m Square Designations for North Polar Zone

MGRS 100,000m Square Designations for South Polar Zone

c. The method for calculating the remainder of the MGRS coordinate is the same as in d (above).

Description of F-16 GRS Coordinates

The F-16 Grid Reference System (F-16 GRS) is a variant of MGRS that is intended to be compatible with the navigation system of the F-16 fighter aircraft. All other users should use standard MGRS coordinates.

At 100,000m precision, an F-16 GRS coordinate string includes two trailing zeros, following the zone number, the zone letter, and the two-letter 100,000m square designation. In a standard MGRS coordinate string, the presence of these zeros would imply 10,000m precision. However, due to a quirk in the F-16 navigation system, strings of this form are used to designate a 100,000m square. Except for this quirk, F-16 GRS coordinates are identical to MGRS coordinates.

Description of USNG Coordinates

The United States National Grid (USNG) is an alpha-numeric system, based upon the UTM and UPS map projections, for identifying positions. An USNG coordinate consists of a zone designation, alphabetic 100,000-meter grid square designator, and numeric coordinates within the 100,000 meter grid square. USNG coordinates are defined for the primary UTM and UPS areas, but not for the overlap areas. USNG coordinates are identical to MGRS coordinates, except that USNG coordinates use a single pattern of 100,000-meter grid square designators (the AA pattern), regardless of the ellipsoid.

In the UTM area, USNG coordinates are based on the ellipsoid, geodetic latitude, UTM zone, Easting and Northing as follows:

a. The first two characters of the USNG coordinate are the two digits of the numeric UTM zone. Leading zeros must be included. The figure below shows the layout of the zones, including the irregular zones in the North Atlantic.

b. The third character of the USNG coordinate is a letter representing a band of geodetic latitude. Beginning at 80°S and proceeding northward, the 20 bands are lettered C through X, omitting I and O. The bands are all 8° high except band X (72°N to 84°N), which is 12° high. The figure below shows the layout of these bands.

USNG Zones and Bands

c. The fourth and fifth characters of the USNG coordinate are a pair of letters representing the 100,000-meter grid square. The diagram below shows the pattern of 100,000 meter square. The patterns are repeated every six zones.

Note: The alphabetic method of designating 100,000-meter grid squares has changed over time. Older products may have different grid square designations.

USNG 100,000m Square Designations (AA Pattern)

d. The remainder of the USNG coordinate string consists of the numeric Easting and Northing values within the 100,000-meter grid square. The left half of the digit sequence is the Easting value, which is read to the right from the left edge of the 100,000-meter grid square. The right half of the digit sequence is the Northing value, which is read northward from the bottom edge of the 100,000-meter grid square. Both the Easting and Northing values are within the range from 0 to 100,000 meters. Both Easting and Northing values must have the same resolution and must include leading zeros.

In the UPS area, USNG coordinates are based on the ellipsoid, geodetic latitude and longitude, Easting, and Northing as follows:

a. The first character of the USNG coordinate is:

A in the Southern and Western Hemispheres,

B in the Southern and Eastern Hemispheres,

Y in the Northern and Western Hemispheres, and

Z in the Northern and Eastern Hemispheres.

b. The second and third characters of the USNG coordinate are letters representing a 100,000 meter grid square. The diagrams below show the layout of the 100,000 meter squares in the north and south polar zones.

USNG 100,000m Square Designations for North Polar Zone

USNG 100,000m Square Designations for South Polar Zone

c. The method for calculating the remainder of the USNG coordinate is the same as in d (above).

# UNCLASSIFIED