projection. The parameters vary by nation or region or mapping 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]
History
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.
Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the
Universal Polar Stereographic
(UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps.
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.
Definitions
UTM zone
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.
Each of the 60 zones uses a
transverse Mercator projection that can map a region of large north-south extent with low distortion. By using narrow zones of 6° of longitude (up to 668 km) in width, and reducing the scale factor along the central meridian to 0.9996 (a reduction of 1:2500), the amount of distortion is held below 1 part in 1,000 inside each zone. Distortion of scale increases to 1.0010 at the zone boundaries along the equator
.
In each zone the scale factor of the central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two
standard lines
, or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard lines and greater than 1 outside them, but the overall distortion is minimized.
Exceptions
The UTM zones are uniform across the globe, except in two areas. On the southwest coast of Norway, zone 32 is extended 3° further west, and zone 31 is correspondingly shrunk to cover only open water. Also, in the region around Svalbard, the zones 32, 34 and 36 are not used, while zones 31 (9° wide), 33 (12° wide), 35 (12° wide), and 37 (9° wide) are extended to cover the gaps.
Overlapping grids
Distortion of scale increases in each UTM zone as the boundaries between the UTM zones are approached. However, it is often convenient or necessary to measure a series of locations on a single grid when some are located in two adjacent zones. Around the boundaries of large scale maps (1:100,000 or larger) coordinates for both adjoining UTM zones are usually printed within a minimum distance of 40 km on either side of a zone boundary. Ideally, the coordinates of each position should be measured on the grid for the zone in which they are located, but because the scale factor is still relatively small near zone boundaries, it is possible to overlap measurements into an adjoining zone for some distance when necessary.
They are however sometimes included in UTM notation. Including latitude bands in UTM notation can lead to ambiguous coordinates—as the letter "S" either refers to the southern hemisphere or a latitude band in the northern hemisphere—and should therefore be avoided.
Locating a position using UTM coordinates
A position on the Earth is given by the UTM zone number and hemisphere designator 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, a false Easting of −500000 meters is added to the central meridian. Thus 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 166000 meters to 834000 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. The southern hemisphere's northing at the equator is set at 10000000 meters. Northings decrease southward from these 10000000 meters to about 1100000 meters at 80 degrees South, the south end of the UTM zones. Therefore, no point has a negative northing value.
For example, the CN Tower is at 43°38′33.24″N79°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; the non-ambiguous format is to specify the full zone and hemisphere designator, that is, "17N 630084 4833438".
Simplified formulae
These formulae are truncated version of
millimeter within 3000 km of the central meridian.[10] Concise commentaries for their derivation have also been given.[11][12]
The
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.
In the following formulas, the distances are in
kilometers
. First, here are some preliminary values:
From latitude, longitude (φ, λ) to UTM coordinates (E, N)
First we 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 (φ, λ)
Note: Hemi = +1 for Northern, Hemi = −1 for Southern