Lat/lon, UTM, & Datum 400
by Larry Sallee
aka Havasu Desert Rat


"Here's just a little bit of my own knowledge to get you started."

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Latitude & Longitude
1.  Latitude and Longitude, often abbreviated as lat/lon, is one of the oldest coordinate systems known, and is still the most well known.  Lat/lon is a grid made up of a series of imaginary lines circling the earth.  Latitude lines run parallel to, and measure distance North and South from, the equator.  Longitude measures the distance east or west from a line running through the village of Greenwich (pronounced Gren-ich), England and through both poles.  On the Greenwich side of the world, this line is known as the Greenwich Meridian or the Prime Meridian, and on the opposite side of the globe, it is known as the International Date Line.  Even though the Prime Meridian runs through Greenwich, the new day starts at the International Date Line.  This was all established in 1884.

2.  Lat/lon are measured in degrees, minutes, and seconds.  Just as a circle has 360 degrees, so has the earth.  Each degree is divided into 60 minutes, which in turn are divided into 60 seconds.  We also need to establish in which direction we are moving.  We have North and South hemisphere for latitude.  Lines North of the equator are obviously North, and the opposite for South.  Longitude is measured from 0 to 180 degrees east or west from the prime meridian.  0° longitude runs through Greenwich and the International Date Line is longitude 180°.

3.  So a typical lat/lon coordinate might be N 33° 38’ 58.8”  W 114° 51’ 11.6”.  You will notice that there is a decimal point with an extra digit after the primary seconds.  This is to obtain more precision.

4.  There are a couple of other formats that can be used to express lat/lon.  These are often referred to as digital lat/lon.  The digital lat/lon is not a hard concept once you understand what is happening.

5.  Let's start with the sample coordinate above.  N 33° 38’ 58.8”  W 114° 51’ 11.6”  This is in the format that you are probably familiar with, H DDD MM SS.s, in other words, hemisphere, degrees, minutes, seconds and tenths of seconds. The various decimal degree formats are just a way to simplify writing this out, and possibly eliminate some confusion. (Or create some confusion, as the case may be.)

6.  To convert these coordinates to H DDD MM.mmm (Hemisphere, degrees, minutes and decimal minutes), you simply divide the seconds portion of the first coordinate by 60 (the number of seconds in a minute), thereby converting it into a decimal form. For example, N 33° 38’ 58.8” becomes N 33° 38.980. (58.8/60=.980) You just put a decimal after the 38 and tack on the results of the division. Same coordinate, but now in decimal form.

7.  You can do the same thing to convert the H DDD MM.mmm to H DDD.dddddd. You take the 38.980 and divide it by 60 (This time, its the number of minutes in a degree) and put the results of the division after a decimal point placed after the primary degrees. Thus, N 33° 38.980 becomes N 33.649667. Again, same coordinate, different and somewhat simplified format.

8.  It is also just as easy to convert the other way.  In order to convert H DDD.dddddd to H DDD MM.mmm, you do just the opposite.  Multiply the decimal degrees by 60 to get minutes and decimal minutes.  And again, multiply decimal minutes by 60 to get seconds.

9.  Going back to our example above, if you take the coordinate N 33.649667 and multiply the part after the decimal by 60, you get minutes.  Don't forget the decimal point.  So .649667*60 = 38.980, which are the minutes, gives us N 33° 38.980'.  If we take it the last step, we multiply .980 by 60 giving us 58.8.  Seconds are generally rounded to the nearest tenth, (So round your answer if necessary.) giving us the coordinate N 33° 38' 58.8", which is where we started.

10.  You should also be aware that there is at least one coordinate system out there, popular on some of the mapping sites like Topozone, in which there isn't a designation for N or W. Instead they use + and -.  North and East are + and South and West are -.  I believe the rest is one of the two decimal designations. I’m afraid I haven't played with these too much. See next paragraph.
 
 

The Universal Transverse Mercator (UTM)

11.  I much prefer the UTM myself, although depending on where you go, it has it's problems also. UTM stands for Universal Transverse Mercator, and was developed by the military.  The UTM is a coordinate system made up of 1,000 meter squares. The baselines for the UTM are the equator and the International Dateline.  For a very good explanation of the details of the UTM system, or if you are using UTM South of the equator, see More Details About the UTM Coordinates System.  I will assume for the following explanation that you are North of the equator.

12.  UTM works very well for most of us, having only a slight distortion that is made up for on the maps. The problem with UTM comes as you get close to the North and South poles. Then it starts to distort considerably. Remember that we are taking a round object and trying to display and measure it on a flat piece of paper.  The UTM is only used as far North as 84° latitude and as far South as 80° latitude.  They have come up with a complementary system, UPS, that is used near the poles.

13.  In UTM, the earth is divided into 60 zones. You will also notice a letter after the zone. If you look at  UTM Grids , it shows a map of the earth with the UTM system overlaid on it and the letters will become self explanatory.

14.  Using the UTM system with a GPS unit couldn’t be simpler.  Most newer maps are being printed with the UTM grid already on them.  Most older maps don’t have the grid itself printed, but have little tic marks (Blue on US maps.) along the sides.  The UTM doesn’t run absolutely North/South, so when connecting the tic marks to create the grid on an older map, make sure that you are connecting matching UTM tic marks.  The UTM numbers next to the tic marks tell the story.

15.  The key to using the UTM coordinate system is to remember that the UTM coordinates run North and East.  Each coordinate given is a measure of how many meters that spot is from the baselines.  You have an Easting, which tells how far East from the International Date Line and a Northing which tells how far North  from the  equator.

16.  The Easting and Northing are each a 7 digit number.  If you look at a typical 1:24,000 scale topo, you will see the primary Easting and Northing numbers printed next to either the grid lines or tic marks.  Each UTM square on the map is 1000 meters on a side.  The first 4 digits tell you which 1000 meter square  you are in, and the final 3 digits tell you how far, North and east, you are into that square.

17.  A quick example:  Given the coordinates – 11  S  0748968    3812890  -  A quick glance tells us that we are in zone 11 in the ‘S’ band.  The first set of coordinates are the Easting and the second set are the Northing.  If you look at the map at the link above, you can tell roughly which part of the world you are in.  Let’s narrow it down a lot further.

18.  Assuming you have the correct 7.5 minute topo (1:24,000), first check the Easting.  The Easting coordinates are printed along the top and bottom of the map with their corresponding lines drawn vertically.  In our example coordinates, we are looking for an Easting of 0748968.  For now, ignore the last three digits.  You are now looking for a line marked with 0748.  It will actually look like 748.  The leading zero is dropped and the digit 7 is printed small because it can typically be ignored since it is usually the same across an entire map.  The 48 will change.  Now, find the corresponding line and put your finger on that line and then give your attention to the Northing.

19.  Our Northing coordinate is 3812890.  Again, ignore the last 3 digits for the time being.  Look along the left or right margins of the map and find a grid line labeled 3812.  It should look like 3812.  Again, the 38 is printed smaller because it will typically be the same across the entire map.

20.  So now, you should have your fingers on two separate lines, one vertical and one horizontal.  Now find where they cross.  That is your starting point to find your exact position.  At a minimum, you have now located your position to within 1000 meters.

21.  Remembering that we are working with coordinates called Easting and Northing, the square that you will be working in is the one to the East and North of the intersection of the 2 lines you located.  You can eyeball the last 3 digits of each of the coordinates to get an approximate location.  The Easting is 968 and the Northing is 890.  Your location is very close to the upper right hand corner of the square you have located.  If you have purchased one of the inexpensive clear plastic grid tools, or if your compass has one built in, you can narrow things down even further.  Place the grid tool over the square in question and measure across 968 and up 890, the distance designated by the coordinates.  With the more accurate grid tools, you can place your location to within 10-20 meters on a topo map.

22.  I highly recommend a grid tool called the Ultimate Trail Mapper.  This handy little tool has the grid marked along all 4 edges and also forming a + through the middle.  This means that you always have a tic mark within 250 meters or less of the position you are trying to mark or locate.  The lines forming the 1,000 meter square extend beyond the intersections making it very easy to position the tool accurately.  It also comes with complete instructions and a sample topo map.

23.  For ordering information on the Ultimate Trail Mapper, please see the contact information at the end of this article.
 
 

Datum

24.  We also need to talk briefly about datums.  A datum is a reference point that is used to 'anchor' a coordinate system or grid.  In the lower left corner of USGS topo maps, you will find a lot of information about the map,
including the datum it is built on.  Most USGS topo maps are based on the North American Datum of 1927.  For you Garmin users, that translates to NAD27 CONUS, or North American Datum, 1927, Continental United States.  There are several other NAD27s listed.  Make sure if you are in the US, you use the CONUS version.

25.  Some newer maps are being based on the WGS 83 which is is very close to the WGS 84.  Again, check your map.  If you have your GPS unit set to a different datum than the one the map is based on, it can throw you off SUBSTANTIALLY! Likewise, if you ever share coordinates with a friend, or a site like geocaching.com, you must make sure that everyone is using the same datum or you are wasting your time.

26.  The very newest datum, and theoretically most accurate, is the WGS 84.  This is the datum that the GPS system is based on and that is used for all internal calculations by your GPS unit.

27.  Now we come to another problem.  Let's say that I am comfortable using the UTM system when navigating in the boondocks.  I also have my unit set to the NAD27 CONUS datum since the maps of my area are based on that datum.  I am playing the geocaching game and having placed a cache, I want to report it to the website and give them the coordinates.  Only problem is that the geocaching website only accepts coordinates in the H DDD MM.mmm format and they require that all coordinates given to them are based on the WGS 84 datum.  Does this mean that I have to change my GPS unit to something that won't match my maps and that I'm not comfortable with while out exploring? Not at all.

28.  Set your GPS unit up however you are comfortable and use the datum that matches your maps.  Anytime you need to share coordinates or you need a different format for a mapping site or for geocaching or whatever, you just convert the coordinates to whatever version you need.  There are basically 2 ways to do this.

29.  The first is, you can go to a website that offers a conversion utility like Jeeps.com's  Coordinate Translation.
To use the site, just enter a coordinate in one of the accepted formats and hit the submit button.  Another page will appear with the converted coordinates.  A bonus is that if you live within the lower 48 states, you also get conversions to another datum and coordinate system.  Personally, I prefer to just let my GPS do the conversions for me.  You will need to check your users manual for details since no 2 models are the same, but essentially you go into your system setup and change the GPS over to whatever coordinate system or datum you need the coordinates converted to. Then, when you go to your waypoints list and view the coordinates of a waypoint, they will be shown in whatever system or datum you specified.

30.  The secret is in the fact that the GPS stores them all the same no matter what.  Remember that the WGS 84 is the internal standard for the GPS unit and that is how all the coordinates are stored.  Similarly, all the coordinates are stored in the same digital format.  The GPS unit then displays them in whatever form you ask.  You can change datums and coordinate systems all day long and nothing changes internally.  The only
thing that changes is how the unit displays the coordinates.

31.  On my Garmin 12, it takes just a few seconds to change from NAD27 CONUS to WGS 84, or from UTM to the geocaching default of H DDD° MM.mmm.  I have also noticed while doing the research for this page that the conversions given by the JEEP page were off a meter or two from what my GPS gave me.  I don't have any authoritative answer as to which is more accurate, but until I find out otherwise, I think I'll stick with my Model 12.  I think it's as easy or easier to use, and I don't have to worry about making any typo's.  Plus it can handle any coordinate system or datum that is in it's system.

32.  Just for fun, here is the exact same location in a couple of different coordinate systems and a couple of different datums.

UTM, NAD27 CONUS  -  11 S  0699159     3725181
UTM, WGS 84  -  11 S  0699080     3725379

H DDD MM.mmm, NAD27 CONUS  -  N 33° 38.976   W 114° 51.144
H DDD MM.mmm  WGS 84  -  N 33° 38.979  W 114° 51.193

33.  As you can see, if you don't get the datum right, you can be in for major problems.  Remember that in the UTM system, those numbers are actually meters.  Take a good look at how far apart those numbers are.  OUCH!

34.  One final little tidbit, only slightly related.  I have had a number of folks ask me how to type in the degree sign (°) since there isn't a key for it.  It's actually very easy.  You hold down the [alt] key and while holding it down, type 0176 on the numeric keypad.  (Not the numbers at the top of the keyboard, but the keypad on the right.)  After you type in the 0176, release the [alt] key and the  (°) will appear.  If you get a different character, first try again to make sure you typed the number correctly.  You have to include the 0.  If that doesn't work, try the Windows Character Mapper.  Most fonts use the same character set, but you may have an odd one.

Happy Navigating.
 

Author:  Larry Sallee

Larry has been teaching map and compass classes for over 15 years and GPS classes for 5 years.  Along with his wife, Sue, they own and operate Venture West, a prospecting and metal detecting shop in Lake Havasu City, Arizona.  They carry many local topo maps, compasses, books on the subject, and the Ultimate Trail Mapper.  Contact Venture West at venturewest@citlink.net or call (928)-453-9004.

"Thanks Larry, for a well written document that seems to tie all the pieces together. Your efforts are appreciated."  Jim Huggins, ALTOS.

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