NGA Office of GEOINT Sciences
`Coordinate Systems Analysis (CSAT)
`Phone: 314-676-9124
`Unclassified Email: coordsys@nga.mil
`March 2007
`
`THE UNIVERSAL GRID SYSTEM
`• Universal Transverse Mercator (UTM)
`• Military Grid Reference System (MGRS)
`• Universal Polar Stereographic (UPS)
`• United States National Grid (USNG)
`A simplified definition and explanation of UTM and related systems
`
`
`
`THE UTM SYSTEM
`
`
`UTM coordinates are based on a family of 120 Transverse Mercator map
`projections (two for each UTM zone, with one for each N/S hemisphere).
`
`
`• The earth is divided into 60 zones, each 6° wide in longitude (with the
`exception of a few non-standard-width zones for Svalbard and
`southwest Norway). See Figure 1.
`
`Figure 1.
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`Coordinate Systems Analysis (CSAT)
`Phone: 314-676-9124
`Unclassified Email: coordsys@nga.mil
`March 2007
`
`THE UNIVERSAL GRID SYSTEM
`• Universal Transverse Mercator (UTM)
`• Military Grid Reference System (MGRS)
`• Universal Polar Stereographic (UPS)
`• United States National Grid (USNG)
`A simplified definition and explanation of UTM and related systems
`
`
`
`THE UTM SYSTEM
`
`
`UTM coordinates are based on a family of 120 Transverse Mercator map
`projections (two for each UTM zone, with one for each N/S hemisphere).
`
`
`• The earth is divided into 60 zones, each 6° wide in longitude (with the
`exception of a few non-standard-width zones for Svalbard and
`southwest Norway). See Figure 1.
`
`Figure 1.
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
`• Numbering of zones begins at 180° and proceeds eastward.
`o Zone 1 is from 180°W to 174°W,
`o Zone 2 is from 174°W to 168°W, and so on.
`• Each zone has a central meridian.
`o Zone 1 central meridian is 177°W,
`o Zone 2 central meridian is 171°W, and so on.
`• The X value, called the Easting, has a value of 500,000m at the
`central meridian of each zone (Figure 2).
`• The Y value, called the Northing, has a value of 0m at the equator for
`the northern hemisphere (Figure 3), 10,000,000m at the equator for
`the southern hemisphere.
`
`
`
`
`
` Figure 2. Easting values. Figure 3. Northing values.
`
`
`
`
`
`• UTM is limited to the area between 84°N and 80°S. Beyond that,
`Universal Polar Stereographic (UPS) coordinates are used. See
`section on UPS.
`
`
`
`
`
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
`REFERENCING / EXPRESSING A POSITION IN UTM COORDINATES
`
`• In the UTM system, positions are expressed as Easting / Northing,
`e.g. “580817mE, 4251205mN”. In some cases, the letters are left off,
`e.g. “580817 4251205”.
`• If positions occur near UTM zone junctions, the UTM zone may also
`be specified, e.g. “580817mE, 4251205mN, Zone 15”.
`• Since the above expresses two possible positions on the earth, the
`hemisphere may also be specified, e.g. “580817mE, 4251205mN,
`Zone 15, Northern Hemisphere” (Figure 4).
`
`
`
`
`
`
`
`Figure 4. Example of position expressed in both Lat/Long and UTM
`coordinates.
`
`• Many systems abbreviate the above, representing the hemisphere as
`a single letter, “N” for northern hemisphere, and “S” for southern
`hemisphere, e.g. “15N 580817 4251205”.
`• CAUTION: IN MANY SYSTEMS, THE LETTER AFTER THE ZONE
`NUMBER DESIGNATES A LATITUDINAL BAND, NOT A
`HEMISPHERE. MORE ON THIS BELOW.
`
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
`MGRS
`
`The Military Grid Reference System (MGRS) is an alpha-numeric system
`for expressing UTM / UPS coordinates. A single alpha-numeric value
`references a position that is unique for the entire earth. The components of
`MGRS values are as follows:
`(Example: 15SWC8081751205)
`
`
`
`• The first two characters represent the 6° wide UTM zone.
`o Leading zeroes are included so that Zone 9 is “09”.
`o For polar areas outside the UTM area, these characters are
`omitted.
`• The third character is a letter designating a band of latitude.
`o Beginning at 80°S and preceding northward, the 20 bands are
`lettered C through X, omitting I and O.
`o The bands are all 8° high except band X, which is 12° high.
`o Outside the UTM area, A and B are used near the South Pole,
`Y and Z near the North Pole.
`
`
`• The vertical UTM boundaries and horizontal latitudinal band
`boundaries form (generally) 6° X 8° Grid Zones. Hence, the first
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
`
`
`
`
`
`three letters of the MGRS value, e.g. “15S”, are referred to as the
`Grid Zone Designator (GZD).
`• The fourth and fifth characters are a pair of letters identifying one of
`the 100,000-meter grid squares within the grid zone (or UPS area).
`See Figure 6.
`
`
`
`Figure 6.
`In this sample area, the Grid Zone Designators are shown in brown.
`The smaller gray letters are the100,000-meter grid square identifiers.
`The example point “15SWC8081751205” is located in square “WC” near
`the center of the figure.
`
`• The remaining characters consist of the numeric Easting and
`Northing values within the 100,000-meter grid square (Figure 7).
`
`• MGRS coordinates may be rounded to reflect lesser refinement. For
`example:
`15SWC8081751205 is at one-meter refinement.
`15SWC80825121 is at 10-meter refinement.
`15SWC808512 is at 100-meter refinement.
`15SWC8151 is at 1000-meter refinement.
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
`• There are two lettering schemes for the 100,000-meter grid square
`identifiers. Generally, one scheme is used for WGS-84, and the other
`is used for older ellipsoids associated with local datum’s. Example:
`15SWC8081751205
`
`is on WGS-84. When converted to NAD-27 datum, Clarke 1866 ellipsoid,
`its value is:
`
`15SWN8083350993
`
`The 100,000-meter grid square “WC” for WGS-84 generally coincides with
`the grid square “WN” for Clarke 1866.
`See the section on USNG for further guidance.
`
`Figure 7.
`Magenta arrows show how MGRS easting and northing values are
`determined from within the 100,000-meter grid square. The MGRS value
`of this position is 15SWC8081751205.
`
`
`
`
`
`
`
`
`
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
` THE LETTER AFTER THE UTM ZONE NUMBER: IS THAT A
`HEMISPHERE OR A LATITUDINAL BAND?
`
`Since the creation of UTM, developers have interpreted the rules for
`expressing an earth-wide unique UTM position in one of two ways:
`
`
`1. By including an “N” or “S” after the zone number to specify a
`hemisphere.
`2. By including the 8° latitudinal band designator (see the section on
`MGRS) after the zone number.
`
`
`Example: The position at 92°W, 38°N, expressed in UTM coordinates, is:
`
`
`587798m E, 4206287m N, Zone 15.
`
`This reference is valid for two positions on the earth. In order to make it
`unique for only one position worldwide, i.e. 92°W, 38°N:
`
`
`• Developer #1 includes an “N” to specify northern hemisphere:
`15N 587798 4206287
`
`• Developer #2 includes the 8° latitudinal band designator:
`15S 587798 4206287
`
`
`This situation is causing confusion among users and developers. The two
`8° latitudinal bands, from 0° to 8°N and from 32°N to 40°N, are assigned
`the designations “N” and “S”, respectively. These designations are often
`mistaken for hemisphere designations.
`
`Technical Manual 8358.1 contains the authoritative definition of UTM. NGA
`will soon publish an updated version of TM 8358.1, which will provide
`clarification on this issue.
`
`
`
`Microsoft Corp. Exhibit 1022
`
`
`
`
`
`THE UNIVERSAL POLAR STEREOGRAPHIC (UPS) SYSTEM
`
`
`UPS coordinates are based on a family of two Polar Stereographic map
`projections, one for each pole.
`
`
`• The origin of the UPS coordinate system is the pole (north or south),
`where X=2,000,000m and Y=2,000,000m.
`• The X-axis lies along the meridians 90°E and 90°W.
`o Moving from the pole (north or south), X-values (Easting’s)
`increase along the 90°E meridian.
`• The Y-axis lies along the meridians 0° and 180°.
`o Moving from the North Pole, Y-values (Northing’s) increase
`along the 180° meridian.
`o Moving from the South Pole, Y-values (Northing’s) increase
`along the 0° meridian.
`
`
`
`
`
`
`
`
`THE UNITED STATES NATIONAL GRID (USNG)
`
`USNG is functionally equivalent to MGRS. The main difference between
`the two systems is in the method for specifying the datum. In MGRS, an
`alternate lettering scheme is used for the 100,000-meter grid square
`designator when the position is referenced to an older datum (see section
`on MGRS). The USNG does not use the alternate lettering scheme, but
`simply specifies the datum after the position reference. For example, a
`position on the NAD 27 datum is reported in the two systems as follows:
`
`
`MGRS: “15SWN8083350993”
`USNG: “15SWC8083350993 (NAD 27)”
`
`Microsoft Corp. Exhibit 1022
`
`
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