The Universal Transverse Mercator (UTM) Coordinate System

Figure 1. The zones used in the UTM spatial coordinate system.

The Universal Transverse Mercator, or UTM, spatial coordinate system has become a favorite among GIS users. Its popularity can be attributed to its nearly worldwide coverage (it excludes only small regions around the poles) and its ease of use. It is not as accurate as the State Plane Coordinate system, but for most uses its accuracy is still quite acceptable.

Figure 2. The globe with UTM zones identified.

The U.S. Army is frequently given credit for creating the UTM system, but the true history is a lot more complex than this brief statement suggests. Basically, after the Second World War, all of the nations in NATO (the North Atlantic Treaty Organization; the group of western nations organized to oppose the Soviet Union and its allies) agreed that a standard spatial coordinate system was needed. As long as each nation's military used their own spatial coordinate system, it would be impossible to precisely coordinate military movements between nations. A standard spatial coordinate system would eliminate this problem. In the early 1950's, with the outbreak of the Korean War, the need for this standard spatial coordinate system became quite acute.

Figure 3. A Transverse Mercator map.

During the five years prior to the outbreak of the Korean war, the British, Portuguese, French and Belgians had recognized the need to develop a spatial coordinate system for mapping Africa (without such a system, the borders of their African colonies would be impossible to locate accurately, and the possibility of armed conflicts arising over boarder disputes could not be dismissed). The civilian governments of these nations had agreed on most aspects of a spatial coordinate system that looked a lot like what would ultimately become the UTM system, but they couldn't agree on how big the zones should be (along with one or two other relatively minor points). Even after a series of conferences held periodically between 1945 and 1951, no agreement could be reached on these last points needed to finalize a standard spatial coordinate system.

Figure 4. The transverse mercator map from Figure 3 with its central meridian highlighted. The central meridian is at -105 degrees longitude.

The U.S. Army's contribution was to adopt the aspects of the spatial coordinate system that the African colonial powers had already agreed upon, and to simply impose standards for the aspects that the colonial powers could not agree upon. With one or two minor changes, the system that the U.S. Army imposed between 1949 and 1951 became the UTM system.

In its final form, the UTM system uses 60 zones, each 6 degrees of longitude wide (Figure 1). Each zone extends from 80°S latitude to 84°N latitude; the reason for the asymmetry is that 80°S just happens to fall very conveniently in the southern ocean, south of South America, Africa and Australia; but you have to go up to 84°N to reach a point north of Greenland (Figure 1). The zones are numbered, starting with 1 which runs from the 180° to the 174°W line of longitude, with numbers increasing as you move west (Figures 1 and 2). Collectively, these zones cover almost the entire planet, omitting only the Arctic Ocean in the north and central Antarctica in the South.

Figure 5. The transverse mercator map from Figure 4 with a UTM zone extending 3 degrees on either side of its central meridian. The zone runs from 84°N to 80°S latitude. This is UTM zone number 13.

As its name implies, the UTM system is based on the Transverse Mercator projection (Figure 3). Each UTM zone utilizes a Transverse Mercator map whose central meridian runs down the line of longitude at the center of the zone (Figure 4). Thus, UTM zone 1, which extends from 180° to 174°W longitude, has a central meridian running down the 177°W line of longitude (Figure 5).

The UTM system doesn't use the "standard" Transverse Mercator projection, which is tangent. Instead, it uses a secant variation that has two lines of tangency located approximately 180 kilometers on either side of the central meridian. Since the ratio of actual map scale to nominal scale is 1.0 only along the map's line(s) of tangency, this ratio must be different from 1.0 along the map's central meridian. The formal definition of the UTM system states that along the central meridian, the ratio of actual map scale to nominal scale must be 0.9996. This value determines the exact locations of the map's lines of tangency.

Figure 6. The UTM zone from Figure 5 isolated from the rest of the map.

As a side note, a popular European spatial coordinate system called the Guass-Krüger is virtually identical to the UTM system, except that it uses a true tangent version of the Transverse Mercator projection (i.e., a projection whose ratio of actual map scale to nominal scale is 1.0 along the map's central meridian) instead of the UTM system's secant variation.

UTM zone maps differ from one another not only in the locations of their central meridians and lines of tangency, but also in the model of the Earth they use. The official definition of the UTM system specifies five different spheroids for use in the various zones; all the UTM zones in the United States are based on the Clarke 1866 spheroid.

One unusual feature of the UTM system is that each zone has two sets of Cartesian coordinates, one for the portion of the zone north of the equator and another for the portion of the zone south of the equator. For the northern portion of each zone, the origin is located on the equator, exactly 500,000 meters west of the zone's central meridian. Since the zones are only about 900,000 meters wide at their widest point, placing the origin 500,000 meters to the west of the zone's centerline (i.e., the zone's central meridian) ensures that all coordinates in the zone will be east of the origin. Furthermore, placing the origin on the equator ensures that all coordinates in the northern hemisphere will be north of the origin. Together, these two facts guarantee that all coordinates (in both the X and the Y directions) in the northern half of each zone will be positive (Figure 7).

Figure 7. UTM zone 13 coordinates for the northern hemisphere.

Coordinates are just slightly more complex in the southern hemisphere. Once again, the origin is placed 500,000 meters west of the map's central meridian, but instead of placing it on the equator, in the southern half of each UTM zone the origin is shifted 10,000,000 meters south of the equator (Figure 8). That puts the origin just about on the South Pole, so once again, all coordinates in the southern half of each UTM zone, in both the X and the Y directions, will be positive.

This duel-origin approach can cause some confusion when using the UTM system. Within each zone, there are two points that have the same coordinates, one point being in the northern hemisphere and the other in the southern hemisphere. In order to distinguish between these two points, UTM zone must be divided north-to-south. In the official definition of the UTM system, each zone is divided into 20 subzones, identified by the letters C through X, omitting the letters I and O (Figure 9). The reason that the system starts with the letter C (rather than A) is because the military uses A and B for special purposes, and a hastily written I looks too much like a one and an O could be confused with a zero. There is also a good reason why the 19 southern subzones (subzones C through W) are each 8 degrees of latitude in width while the northernmost subzone (subzone X) is 12 degrees of latitude wide. When the original UTM definition was published by the U.S. Army in 1951, each UTM zone only extended to the 80°N line of latitude. Under this original scheme, each subzone was 8° of latitude wide. However, when it became clear that the 80°N cutoff was causing problems because it truncated areas in northern Greenland and Russia, UTM zones were extended to 84°N. Rather than change all the subzones to accommodate this expansion, only the northernmost subzone -- subzone X -- was extended.

Figure 8. UTM zone 13 coordinates for the southern hemisphere.

In all honesty, outside of the military, this complex system of 20 north-to-south subzones is rarely used. Instead, an unofficial system of dividing UTM zones into only two subzones -- one north of the equator, the other south of it -- is very widely used. This adds another source of confusion, because in the two-subzone system, the northern subzone is frequently called (logically enough) subzone N and the southern subzone is called subzone S. Unfortunately, the official 20-subzone system also has subzones N and S, but they don't correspond to the S and N subzones in the two-subzone system. If fact, in the official 20-subzone system, both subzones S and N are in the northern hemisphere, and subzone S is farther north than subzone N. The onus is on you to know which system of subzones -- the official 20 subzone system or the unofficial 2-subzone system -- is being used in any given situation.

The official UTM definition calls for all coordinates within any given UTM zone to be measured in meters east or west of the zone's origin. The distances east of the origin, which in a Cartesian coordinate approach would be called the X coordinates, are typically called eastings. Similarly, distances north of the origin, which in a Cartesian coordinate approach would be called the Y coordinates, are typically called northings.

The UTM system's accuracy is rated as one in twenty five hundred (this is usually written as 1:2,500). This means that if you use UTM coordinates to measure a line as being 2,500 units long (you can use any units you'd like -- this measure of accuracy is not dependent upon any fixed units of measure), you may be off by as much as one unit -- the line might be anywhere from 2,499 to 2,501 units in length. This is four times less accurate than the State Plane Coordinate system, whose accuracy is rated as 1:10,000.

Figure 9. Official UTM north-to-south subzones.