Universal Transverse Mercator Coordinate System
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Universal Transverse Mercator Coordinate System


Most zones in UTM span 6 degrees of longitude, and each has a designated central meridian. The scale factor at the central meridian is specified to be 0.9996 of true scale for most UTM systems in use.[1][2]

UTM zones on an equirectangular world map with irregular zones in red and New York City's zone highlighted


The National Oceanic and Atmospheric Administration (NOAA) website states that the system was developed by the United States Army Corps of Engineers, starting in the early 1940s.[3] However, a series of aerial photos found in the Bundesarchiv-Militärarchiv (the military section of the German Federal Archives) apparently dating from 1943-1944 bear the inscription UTMREF followed by grid letters and digits, and projected according to the transverse Mercator,[4] a finding that would indicate that something called the UTM Reference system was developed in the 1942-43 time frame by the Wehrmacht. It was probably carried out by the Abteilung für Luftbildwesen (Department for Aerial Photography). From 1947 onward the US Army employed a very similar system, but with the now-standard 0.9996 scale factor at the central meridian as opposed to the German 1.0.[4] For areas within the contiguous United States the Clarke Ellipsoid of 1866[5] was used. For the remaining areas of Earth, including Hawaii, the International Ellipsoid[6] was used. The World Geodetic System WGS84 ellipsoid is now generally used to model the Earth in the UTM coordinate system, which means current UTM northing at a given point can differ up to 200 meters from the old. For different geographic regions, other datum systems can be used.


The transverse Mercator projection is a variant of the Mercator projection, which was originally developed by the Flemish geographer and cartographer Gerardus Mercator, in 1570. This projection is conformal, which means it preserves angles and therefore shapes across small regions. However, it distorts distance and area.


UTM zone

Simplified view of contiguous US UTM zones, projected with Lambert conformal conic.

The UTM system divides the Earth into 60 zones, each 6° of longitude in width. Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174°E to 180°. The polar regions south of 80°S and north of 84°N are excluded.



Overlapping grids

Universal Transverse Mercator (UTM) Grid Zones 31N thru 37N differ from the standard 6° wide by 84° zone for the northern hemisphere, in part to accommodate the southern half of the Kingdom of Norway. For more on its history, see Clifford J. Mugnier's article on Grids & Datums of The Kingdom of Norway that appeared in the October 1999 issue of PE&RS http://www.asprs.org/a/resources/grids/10-99-norway.pdf


Latitude bands

Latitude bands are not a part of UTM, but rather a part of the military grid reference system (MGRS).[7] They are however sometimes used.

Latitude bands




The combination of a zone and a latitude band defines a grid zone. The zone is always written first, followed by the latitude band. For example, (see image, top right), a position in Toronto, Ontario, Canada, would find itself in zone 17 and latitude band "T", thus the full grid zone reference is "17T". The grid zones serve to delineate irregular UTM zone boundaries. They also are an integral part of the military grid reference system.




Locating a position using UTM coordinates

A position on the Earth is given by the UTM zone number and the easting and northing planar coordinate pair in that zone. The point of origin of each UTM zone is the intersection of the equator and the zone's central meridian. To avoid dealing with negative numbers, the central meridian of each zone is defined to coincide with 500000 meters East. In any zone a point that has an easting of 400000 meters is about 100 km west of the central meridian. For most such points, the true distance would be slightly more than 100 km as measured on the surface of the Earth because of the distortion of the projection. UTM eastings range from about 167000 meters to 833000 meters at the equator.

In the northern hemisphere positions are measured northward from zero at the equator. The maximum "northing" value is about 9300000 meters at latitude 84 degrees North, the north end of the UTM zones. In the southern hemisphere northings decrease southward from the equator, set at 10000000 meters, to about 1100000 meters at 80 degrees South, the south end of the UTM zones. For the southern hemisphere, its northing at the equator is set at 10000000 meters so no point has a negative northing value.

The CN Tower is at 43°38?33.24?N 79°23?13.7?W﻿ / ﻿43.6425667°N 79.387139°W﻿ / 43.6425667; -79.387139﻿ (CN Tower), which is in UTM zone 17, and the grid position is 630084 m east, 4833438 m north. Two points in Zone 17 have these coordinates, one in the northern hemisphere and one in the south; one of two conventions is used to say which:



Simplified formulae

These formulae are truncated version of Transverse Mercator: flattening series, which were originally derived by Johann Heinrich Louis Krüger in 1912.[9] They are accurate to around a millimeter within 3,000 km of the central meridian.[10] Concise commentaries for their derivation have also been given.[11][12]

The WGS 84 spatial reference system describes Earth as an oblate spheroid along north-south axis with an equatorial radius of km and an inverse flattening of . Let's take a point of latitude and of longitude and compute its UTM coordinates as well as point scale factor and meridian convergence using a reference meridian of longitude . By convention, in the northern hemisphere km and in the southern hemisphere km. By convention also and km.


From latitude, longitude (?, ?) to UTM coordinates (E, N)

First let's compute some intermediate values:

The final formulae are:

where is Easting, is Northing, is the Scale Factor, and is the Grid Convergence.

From UTM coordinates (E, N, Zone, Hemi) to latitude, longitude (?, ?)


First let's compute some intermediate values:

The final formulae are:

See also


  1. ^ "Universal Transverse Mercator (UTM)". PROJ coordinate transformation software library.
  2. ^ Snyder, John P. (1987). Map projections: A working manual. U.S. Government Printing Office.
  3. ^ "NOAA History - Stories and Tales of the Coast & Geodetic Survey - Technology Tales/Geodetic Surveys in the US The Beginning and the next 100 years". www.history.noaa.gov. Retrieved 2018.
  4. ^ a b BUCHROITHNER, Manfred F.; PFAHLBUSCH, René. Geodetic grids in authoritative maps-new findings about the origin of the UTM Grid. Cartography and Geographic Information Science, 2016
  5. ^ Equatorial radius 6,378,206.4 meters, polar radius 6,356,583.8 meters
  6. ^ Equatorial radius 6,378,388 meters, reciprocal of the flattening 297 exactly
  10. ^ Karney, Charles F. F. (2011). "Transverse Mercator with an accuracy of a few nanometers". J. Geodesy. 85 (8): 475-485. arXiv:1002.1417. Bibcode:2011JGeod..85..475K. doi:10.1007/s00190-011-0445-3. S2CID 118619524.

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