MDARC - Latitude, Longitude, UTM

Latitude, Longitude, UTM

Finding your way around on this planet, especially if you’re away from cities & towns, often requires the use of a geographic coordinate system, of which there are several. Such a system enables every point on Earth to be specified by a set of numbers, letters and/or symbols. A complete coordinate specification locates a particular point in 3-dimensional space. For the surface of the Earth, that would include dimensions north-south; east-west; and elevation or altitude. We often ignore elevation, as it’s usually not important for our need when we’re staying on the surface.

There are numerous geographic coordinate systems available, each taking its own approach to locating a specific point. Each has its own advantages and disadvantages. This page will focus on two of the most popular. In our Further Information section below are links to pages with more information on these two as well as other systems.

References

We all learned while studying for our first ham radio license that there is no absolute voltage level. Voltage is always measured in relation to a reference level; usually some point in the circuit we call “ground”. We define that “ground” level to be zero and measure every other point as a positive or negative amount away from that reference. When we measure somewhere other than from ground (for example, across a resistive device in the middle of the circuit), we must be careful to state that; perhaps by saying that we have a “voltage drop of x volts across that resister”. But even then, we’re actually measuring the voltage of one side of the resister in relation to the voltage on the other side. So it is with geographic coordinate systems. All must have a reference (actually three or more), and every other point on the planet’s surface is located in relation to those references.

North-South Reference

The most fundamental reference for coordinate systems is the equator. Wikipedia defines the equator as “the imaginary line on the spheroid (Earth), equidistant from its poles, dividing it into northern and southern hemispheres.” This provides the zero reference for north-south coordinates.

East-West Reference

The east-west zero reference is an imaginary line perpendicular to the equator; running between the north and south poles; and is usually called a “prime meridian”. By international agreement, the International Prime Meridian runs through the British Royal Observatory in Greenwich, in southeast London, England. Other prime meridians are occasionally used for specific purposes.

Elevation Reference

The third zero reference is for elevation. The most common reference used is Mean Sea Level. Elevations using this reference are typically stated using the acronym AMSL, or Above Mean Sea Level. Calculating just what the mean, or “average”, level is for all the seas in the world is a very complicated process, far beyond the scope of this page, or the understanding of most people.

Geodetic Datum and Projections

Datum

The Earth is not a perfect sphere. It’s not even a perfect ellipsoid (a 3-dimensional oval). This makes the lives of geographers and map-makers a lot harder. For example, exactly what is “vertical” and “horizontal” on an irregularly curving, mountainous surface such as the Earth? To simplify the hard math that would otherwise be impractical, map-makers select a “reference ellipsoid” to approximate the Earth’s surface. They then choose the most appropriate mapping of an essentially spherical coordinate system onto this ellipsoid. Together, this is called a “geodetic datum”. As with coordinate systems, several have been invented. Each will put the same coordinate numbers in a somewhat different location than the others; sometimes differing by tens to over a hundred meters. One datum is called the World Geodetic System, 1984 (WGS 84), and is the default datum used for the Global Positioning System (GPS). For this reason, should you encounter an app or computer program that asks you to select a datum; we recommend you choose WGS 84.

Projections

As long as humans have been making maps and traveling from one point to another, we’ve struggled to find an accurate way to translate shapes (e.g., continents) and long distances on a curved surface like the Earth and show them on a flat surface like a map. This has led to the invention of several “projections”. One of the more well known projections is the Mercator Projection, for example. No projection is perfect, as each distorts some things while more accurately showing others. So if you’re going to use maps a lot, it would be a good idea to learn about the different projections and select one that best serves your need.

Latitude & Longitude

Latitude/Longitude is the most well known and popular geographic coordinate system in the world. Its units of measure are degrees of angle. Degrees can be subdivided into the smaller units of minutes and seconds. There are 360 degrees in a full circle; 60 minutes in a degree and 60 seconds in a minute. The symbol for degrees is a superscript zero (0). The symbol for minutes is an apostrophe (‘); while the symbol for seconds is the quote mark (“).

Imagine you’re standing at the exact center of the Earth, looking out at the surface from the underside as your friend stands at some point on the surface. You then draw a straight line from where you are at the Earth’s center to where your friend is standing on the surface; and a second straight line to the equator directly above or below your friend. The angle created by the two lines you’ve drawn is a portion of a circle (ϕ in the diagram at right), and so can be measured in degrees and its fractions, thus creating a north-south coordinate number we call “latitude”. The maximum value of any latitude measure is 90 degrees. The North Pole is 900 North and the South Pole is 900 South. The equator is 00, both north and south.

Now imagine you draw a third straight line; this one to the prime meridian at the point where it crosses the equator. The angle created by this line and your second line above is another portion of a circle (λ in the diagram at right), also measured in degrees and its fractions, called “longitude”. The maximum value of any longitude measure is 1800, or half of the circle. The meridian line directly opposite the prime meridian on the Earth is both 1800 East and 1800 West. Don’t confuse this 1800 meridian with the International Date Line, which diverges from it in several places for political and convenience reasons; for example to keep all islands of a chain in the same time zone.

The combination of these two latitude & longitude components specifies the position of any location on the surface of Earth, ignoring elevation. The origin/zero point of this system (latitude 00, longitude 00) is on the equator in the Gulf of Guinea about 625 km (390 mi) south of Tema, Ghana, Africa.

Coordinates in the latitude/longitude system can be expressed in three ways: a) degrees and decimal-degrees; b) degrees, minutes and decimal-minutes; or c) degrees, minutes, seconds and decimal-seconds. For example, coordinates for the approximate mid-point of San Francisco’s Golden Gate Bridge may be written as any of the following, all equivalent:

a) N 37.81988°, W 122.47848°
b) N 37° 49.193', W 122° 28.709'
c) N 37° 49' 11.58", W 122° 28' 42.54"

Note there are a couple of variations you may see in the way the above coordinates are written:
1.) The direction symbols (“N” and “W” in the above example) may be placed after the number; as in:
37.81988° N, 122.47848° W.
2) The direction symbols may be omitted, and the negative sign (“-“) used for latitudes south of the equator and longitudes west of the prime meridian; as in: 37.81988°, -122.47848°. This method is often used for data entry into a computer formula or database.

UTM
The Universal Transverse Mercator (UTM) is another geographic coordinate system you should be aware of. It’s less useful for very long (e.g., multi-state or continental) distances, but can be quite accurate for smaller distances; for example, within the San Francisco Bay Area. Another advantage of UTM is that calculating the distance between two points on UTM-based maps can be performed more easily in the field than by using the trigonometric formulas required under the latitude/longitude system. Further, coordinate designations are given in meters, making them easier to understand.

UTM Zones
UTM divides the earth into 60 zones. The zones are imaginary bands that run most of the way between the North and South Poles. (The polar regions south of 80° S and north of 84° N are excluded.) Each zone is 6 degrees wide in longitude, thus covering the full 3600 of the Earth’s surface. Zone 1 begins at longitude 1800 (directly opposite the International Prime Meridian) and ends 60 east of there, at 1740 W longitude. The San Francisco Bay Area and most of northern California are in Zone 10, covering 1260-1200 W longitude.

Easting and Northing
The UTM system uses the concept of “easting and northing” to designate the x & y coordinates within a UTM zone, and so locate a specific point on the Earth’s surface. Although confusing at first, once understood, it can simplify location notation, since it a.) eliminates reference to two of the four compass directions (“S” and “W”); b.) uses easily understood x & y coordinates, with meters as its units, rather than more difficult angular degrees; and c.) eliminates negative coordinate references, as discussed in the Central Meridian and Southern Hemisphere sections below.

In the northern hemisphere, “northing” positions are measured in meters northward from zero at the equator. The maximum "northing" value is about 9,300,000 meters at latitude 840 N. The Golden Gate Bridge’s northing position is 4185959mN; or 4,185,959 meters north of the equator. Similarly, the “easting” coordinate is the number of meters from the UTM zone’s Central Meridian.

Central Meridian
Rather than using a “zero reference” as in the latitude/longitude system, each UTM Zone has a “point of origin”. The point of origin is the intersection of the equator and the zone's central meridian. Northing coordinates are measured from the equator and Easting coordinates are measured from the central meridian. The point of origin for San Francisco’s zone 10 is 00 N latitude, 1230 W longitude.

Using the central meridian as a zero reference, however, would create negative coordinates. To avoid that, the central meridian is defined to have a value of 500,000 Easting. So locations west of the Central Meridian have easting coordinates less than 500,000 while those east of the Central Meridian are greater than 500,000. The Golden Gate Bridge’s easterly coordinate is 545899mE, and so is 45,899 meters east of longitude 1230 W (our central meridian).

Southern Hemisphere
In the southern hemisphere, the UTM system is modified slightly, again to avoid the use of negative coordinates. Instead of referring to the equator as zero meters northing, as it is for the northern hemisphere; the equator is defined with a value of 10,000,000 Northing; similar to the Central Meridian definition for easting.

Latitude Bands
Although technically part of the Military Grid Reference System (MGRS) instead of the UTM system, latitude bands are sometimes used in UTM. There are 20 latitude bands, each 80 high, extending from 800 south latitude to 840 north latitude. The northern-most band is extended an extra 40 to encompass all landmass in the northern hemisphere. These bands are designated with the English alphabet letters “C” through “X”; omitting the letters "I" and "O" because of their similarity to the numerals one and zero. Band C begins at 800 S and band X ends at 840 N. (Latitude bands "A" and "B", along with bands "Y" and "Z", cover the western and eastern sides of the Antarctic and Arctic regions respectively.)

When using the latitude band system, the combination of a UTM zone and a latitude band defines a grid zone. The UTM zone is written first, followed by the latitude band. Thus, the San Francisco Bay Area is in grid zone “10S”.

Complete UTM Coordinate Notation

A complete UTM coordinate notation includes the UTM zone, followed by the Easterly coordinate, then the Northerly coordinate. However, these alone are insufficient, as there are two points that meet these designations; one each in the northern and southern hemispheres. There are two ways to clarify this:

a.) append a hemisphere designator to the zone number, "N" or "S"; or

b.) append a latitude band designator to the zone number, “C” through “X”.

So the complete Golden Gate Bridge UTM location for each method above is:

a.) 10N 545899mE 4185959mN (Hemisphere designator)

b.) 10S 545899mE 4185959mN (Latitude Band designator)

Use of this system can cause confusion, however, as illustrated by the Bridge’s latitude band. Depending on which method is used, “S” can refer to either the southern hemisphere or the latitude band “S”; so method b.) above could indicate to some people that the Golden Gate Bridge is in the southern hemisphere. This makes it important to always state your designation method.

In addition, since the easting coordinate is always given first, followed by a space and the northing coordinate; the "mE" and "mN" in the above locations aren't really needed and are often omitted. In fact, they must be omitted for use in Google Earth, for example. This would give the Golden Gate Bridge location as:

a.) 10N 545899 4185959

b.) 10S 545899 4185959

=======================================

So where is the Golden Gate Bridge again?

1.) N 37.81988°, W 122.47848°

2.) N 37° 49.193', W 122° 28.709'

3.) N 37° 49' 11.58", W 122° 28' 42.54"

4.) 37.81988° N, 122.47848° W.

5.) 37° 49.193' N, 122° 28.709' W

6.) 37° 49' 11.58" N, 122° 28' 42.54" W

7.) 37.81988°, -122.47848°

8.) 37° 49.193', -122° 28.709'

9.) 37° 49' 11.58", -122° 28' 42.54"

10.) 10N 545899mE 4185959mN (Hemisphere designator)

11.) 10S 545899mE 4185959mN (Latitude Band designator)

12.) 10N 545899 4185959 (Hemisphere designator)

13.) 10S 545899 4185959N (Latitude Band designator)

Not to mention the U.S. National Grid (USNG), Military Grid Reference System (MGRS); Universal Polar Stereographic (UPS) system; various circular and spherical angular systems and others.

Eh, it’s all the same to me.

Further Information

Wikipedia:

Geographic coordinate system

Geodetic datum

Universal Transverse Mercator coordinate system

https://en.wikipedia.org/wiki/Military_grid_reference_system

Transverse Mercator projection

Universal Polar Stereographic coordinate system

FCC page: Conversion of Degrees Minutes Seconds to/from Decimal Degrees

Article: How to get GPS coordinates of your location using your Smartphone (medium.com)

Note: All images on this page are provided courtesy of Wikipedia and Wikimedia Commons.

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