UTM, MGRS and the USNG

Contents

• Introduction
• UTM Coordinate & MGRS Grid References
  • A UTM reference
  • An MGRS (or USNG) reference
• The MGRS grid letters
  • MGRS Grid Letters and the Ellipsoid
• Conversion Between UTM and MGRS
  • UTM is Map Projection
  • MGRS is a notation
  • MGRS has a wider Range: UPS
  • Modified Zones around Norway
• Zone and ZDL Boundaries
• MGRS and the United States National Grid (USNG)
• Notes
• Links

Introduction

This page was written for world-wide users of GPS equipment who are interested in understanding more about the numbers generated by their equipment.

It addresses several issues:

• What is UTM, as used on GPS receivers? What use is it? Where did it come from?
• How do you read read/write a UTM reference?
• What is MGRS? What is its relation to UTM? Where did it come from?
• The new United States National Grid is closely related to MGRS: what are the differences?
• How do you convert between UTM, MGRS and USNG?

Some of these questions can be briefly answered:

• UTM stands for Universal Transverse Mercator and is a Map Projection*: that is it is a way to represent the surface of the earth more or less accurately on a flat surface by way of a rectilinear grid (ie it defines grid coordinates). It says nothing about how these coordinates should be written down.
• MGRS is a notation based on UTM which uses letter pairs to designate 100km grid squares together with optional digits to identify a point to arbitrary accuracy within one such square.

The history still remains obscure. It seems that MGRS was adopted by the United States Military around 1950. The Transverse Mercator Projection is much, much older. If anyone knows where the Universal projection came from, mail me!

For a more detailed look, the answer to the remaining questions, and more, read on...

* More accurately it is a set of such projections – one for each of 60 Zones.

UTM Coordinate & MGRS Grid References

First, a summary of terminology:

A UTM reference

has three parts:

1. A Zone. The Earth is divided into 60 Zones divided by meridians (lines of longitude) 6° apart. Zone 1 is bounded by 180°W and 174°W, Zone 2 by 174°W and 168°W and so on to Zone 60, 174°W to 180°W
2. An Easting. Roughly speaking the Easting measures the distance from the central meridian of the zone to the point of interest in meters. To avoid negative values, the meridian itself is given the easting 500,000m: a point 1m east of the meridian has an easting of 500,001m, while a point 1m west has an easting of 499,999m
3. A Northing. Roughly speaking the Northing measures the distance from the Equator to the point of interest in meters. Points south of the equator are written in complementary ("odometer") form: a point 1m south of the equator has northing 9,999,999m and so on down. Since the distance from the equator to the South Pole is slightly less than 10,000,000m, this ensures that the "Northing" in the Southern Hemisphere is unambiguously represented by a positive number.

   However, for any point in the Southern Hemisphere, there will be a point in the Northern Hemisphere (roughly 90° further north) with the same UTM Northing: when quoting a UTM reference it is important to specify the relevant Hemisphere (N or S)

An MGRS (or USNG) reference

(See TM8358.1 Sec 3.4) has four parts:

1. A Zone This is the same as the UTM zone
2. A Latitude Band (not Bond! – that was one of many misprints in TM8358.1 – duplicated ad nauseam on the Web). This is a single letter from C through X depending on the latitude. known as the Zone designation letter or ZDL.
   Sometimes the Zone and the ZDL are regarded as a single entity, the Grid Zone designation or GZD.
3. An MGRS square defined by two letters, and representing a 100km square within the zone. For details on how to obtain these letters see below
4. An Easting measuring the distance from the western edge of the MGRS square to the point of interest
5. A Northing measuring the distance from the southern edge of the MGRS square to the point of interest

The MGRS easting and northing must have the same number of digits, and leading digits (including zeros) must be shown. For example, according to information in the USNG standard, the Washington Monument in Washington, DC, USA has the UTM coordinates:

Zone 18 323483.168mE 4306479.498mN

(to the nearest millimeter! – see Washington Monument Address). According to the convertor, this UTM reference is in Zone 18 with MGRS letters UJ. Its one-meter MGRS reference is therefore 18SUJ2348306479.

Unlike the UTM, the MGRS digits can be truncated from the right. Thus you can write:

18SUJ20
18SUJ2306
18SUJ234064
18SUJ23480647
18SUJ2348306479

MGRS (but not the current specification for USNG) also allows:

18S
18SUJ

USNG allows arbitrary refinement in accuracy:

18SUJ234831064794
18SUJ23483160647949
18SUJ2348316806479498

TM8358.1 only gives examples down to 1m accuracy, so presumably this is the highest resolution allowed.

Note that USNG (but not MGRS) allows the insertion of spaces: you can write 18S UJ 234064 or 18S UJ 234 064 for a USNG. This is a great improvement.

MGRS (and USNG) can also be truncated from the left – but only to a limited degree. As we shall see THE MGRS square letters repeat every 36° of longitude (about 4000km) and every 2000km in a northerly direction. It is the Grid Zone Designation that ties down the exact MGRS square to be referred to. If you don't care about the fact that there is another square of the same name 2000km away, you can omit the Grid Zone Designation. Similarly, if all your interest is in the same MGRS square, and you don't care that there is another point with the same MGRS digits 100km away, you can omit the MGRS square letters as well.

You must not truncate the MGRS digits from the left!

The MGRS grid letters

As I said above, an MGRS square is defined by two letters, and represents a 100km square within the zone. Working out what these letters are is completely straightforward, but tedious, and possibly prone to error. For this reason you may prefer to refer for example to my

Tables of MGRS grid letters

If you would rather do it for yourself, read on...

To obtain the first letter of the MGRS square, each UTM zone is divided into 100km vertical bands, whose edges coincide with 100km multiples of the UTM Easting. Thus for example the middle two bands in each Zone cover Eastings of 400-500km and 500-600km. The width of a zone is about 666km at its widest (ie at the equator), so we require at most 8 such bands to span the width of an entire zone – 6 full bands and two more to cover on half of the remaining 66km each. These 8 bands are rather neatly identified by the following labelling scheme: take the letters of the alphabet less I and O (as being confusable with digits), leaving 24 letters to label the bands of 3 consecutive zones A...H, J...R and S...Z. If we start at zone 1 (180°W long) with A...H, we get the following scheme:

The sequence repeating after every 3 zones. The "Easting" of the band in the table is just the UTM Easting of its western (left-hand) edge in units of 100km.

As we have seen, at the equator bands A,H, J,R, S,Z will be incomplete. At the latitude of Washington the Zone width has shrunk to about 524km and these bands do not appear at all; bands B,G, K,Q, T,Y etc are then incomplete.

To obtain the second letter of MGRS square, we also divides each UTM zone into 183 100km high horizontal bands, labelled with a repeating sequence of the 20 letters A...V, (again excluding I and O), starting at the equator with A in odd numbered zones, but with F in even ones:

This table shows just the first three bands above the equator in the Northern Hemisphere. The "Northing" of a band in the table is of course the UTM Northing of its southern (lower) edge in units of 100km.

Since in any column the second letter remains the same, the MGRS letters repeat in a northerly direction every 2000km. There can be as many as 10 MGRS squares with the same letters in the same Zone: hence the Zone Designation Letter, which is more than sufficient to identify a particular MGRS square of these 10.

In an east-west direction, since the first letter repeats every three Zones, and the second letter repeats every two Zones, the whole sequence repeats every six Zones, ie every 36° of longitude – about every 4000km at the equator. If there is a chance of confusion this is easily resolved by quoting the Zone number.

MGRS Grid Letters and the Ellipsoid

I have deliberately tried to avoid this here, but the precise UTM coordinates depend on the exact ellipsoid taken to represent the shape of the Earth. The specification of this ellipsoid forms part of a map or other coordinate reference Datum. For maps, a description of the Datum should be found in the margin of the map. GPS devices normally provide a mechanism for selecting an appropriate Datum. Choosing a different Datum can result in significantly different UTM coordinates for the same point on the Earth – often of the order of several hundred meters.

Quite apart from this, for some strange reason the MGRS letters chosen to represent a particular 100km square actually depend on the Ellipsoid (and hence the Datum) chosen. Indeed:

The method for obtaining the second MGRS (but NOT USNG) Grid Letter described above does not apply for the North-American NAD27 Datum, which has been widely used on North-American maps. It does apply to the more recent North-American NAD83 Datum, and to almost every other datum you are likely to come across, including the ubiquitous WGS84. I stress that this does not apply to USNG which uses the same "MGRS" letters whatever the datum. This is an important area where MGRS and USNG disagree.

The "Alternate" choice of the second MGRS Grid Letter as used for the NAD27 Datum is essentially the same as that described above, except that it starts at L (for odd-numbered) and R (for even-numbered) zones, instead of A and E respectively, ie the repeating cycle is advanced by 10 letters (remember that I and O are not used).

To summarize, in Odd-numbered zones the MGRS 100km square 2nd letter for most ellipsoids starts at A for the square immedialely above the equator. For other ellipsoids and Zones the letter is advanced:

At present my Maps, Tables of Grid Letters, and Coordinate Convertor are all based on the "standard" WGS 84/NAD83 labelling.

Conversion Between UTM and MGRS

Details are given in TM8358.1. However, if you really want to know how the conversion works, the best way to get at the nitty-gritty is to write (or examine) a simple program to do it. I have written just such a program, together with notes: see my

UTM-MGRS convertor

It is worth pointing out here that the conversion is not simple partly because, as mentioned in the introduction, UTM and MGRS do not try to do the same thing:

UTM is a Map Projection

...Which defines a coordinate system. There is no standard way of representing a UTM reference. However, the coordinates (Easting and Northing) are always quoted in meters. It follows that UTM coordinates are just numbers. They:

1. do not necessarily require leading zeros
2. do not necessarily have to have the same length as each other
3. do not necessarily require a decimal point
4. must not be truncated

In fact the coordinates cannot be truncated from the right like MGRS coordinates, because for example a northing 463000 means 463000.000 meters, while 463 means 463.000 meters, always.

MGRS is a notation

It merely defines a uniform way of representing coordinates, usually UTM coordinates (but see below).

However, any MGRS reference actually defines a square. Just as the MGRS reference 18SUJ defines a 100km square, 18SUJ00 defines a 10km square, and 18SUJ0000 defines a 1km square and so on, all of whose SW corners coincide.

MGRS has a wider Range

MGRS is only defined in terms of UTM in the latitudes 80°S to 84°N. Outside this range MGRS is still defined, but in terms of a different map projection – UPS – and USNG is not defined at all. However, UPS is not only defined outside the geographical range of most of my readers – it must remain at present outside the range of these notes.

The MGRS zones are "bent" around Norway

Some jiggery-pokery was done to make the zones fit more easily around southwest Norway and Svalbard: see the notes below for details. Neither my Maps, Tables of Grid Letters or Coordinate Convertor make allowance for this Zone-bending.

Zone and ZDL Boundaries

A UTM reference is not necessarily unique

More to come...

MGRS and the United States National Grid (USNG)

The United States now has its own National Grid: see

Standard for a United States National Grid, FGDC-STD-011-2001

According to the Federal Standard, USNG is "interoperable" with MGRS. However, elsewhere the defining body has gone out of its way to assert that USNG is only "based" on MGRS. The latter statement is possibly nearer the truth. Many of the differences are mentioned above, but here is a list:

1. USNG allows the use of only two datums, NAD83 (equivalent to WGS84) or NAD27. MGRS allows any number of Datums
2. USNG uses the NAD83/WGS84 datum by default. If you're using NAD27 you must explicitly specify it, eg 18SUJ2306 (NAD 27). MGRS has no default datum, and there is no formal way of specifying which datum is being used (but see the next item)
3. USNG applies the same lettering scheme to its 100 km squares regardless of map datum. MGRS shifts the northing letter 10 places when using eg the NAD27 datum
4. USNG has unlimited precision. MGRS goes no finer than 1 meter
5. USNG allows an "informal" style with spaces in written coordinates, e.g., 18T WL 807 046. Officially, this is forbidden in MGRS. Everything is supposed to be mashed together: 18TWL807046
6. MGRS allows large-area references such as 18S (Grid Zone Designation only) and 18S UU (MGRS square). USNG requires at least two digits following the MGRS square letters.
7. MGRS makes special allowance for Zones in the neighborhood of Norway, see note below. USNG only covers the United States including outlying territories and possessions, so these special zones are not applicable since it has no territories or possessions in these areas (at the present time).
8. MGRS is defined for the whole world: in the latitude range 80°S and 84°N it is defined in terms of UTM, but outside this range it is defined in terms of UPS. USNG, because of its limited range, has no need of UPS and is defined entirely in terms of UTM

Notes

Acknowledgement

Thanks to Paul Hirose for drawing my attention to points 1-4 above.

Zones around Norway

From TM8358.1, 3-2.2.1:

"Zone 32 has been widened to 9° (at the expense of zone 31) between latitudes 56° and 64° to accommodate southwest Norway. Similarly, between 72° and 84°, zones 33 and 35 have been widened to 12° to accommodate Svalbard. To compensate for these 12° wide zones, zones 31 and 37 are widened to 9° and zones 32, 34, and 36 are eliminated."

I have seen a nice map of this somewhere, but I cannot lay my hands on it: does anyone know where I can find it?

Links

Revised 2004-05-30, 2005-08-14

Uprated to xhtml 2005-08-16