# GPS coordinate problem

I have coordinates for a travel site in the WGS84 format:

6413180-2059501

The location is supposed be a cave in Iceland but Google Maps points(after adding a decimal point) to a site in Sweden.

What am I doing wrong?

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do you need the coordinates specifically, or would a map of where the cave is do? – Mark Mayo Aug 14 '12 at 20:17

WGS84 isn't a "format" at such, it's a "projection". Sometimes it's called a "Datum". Sometimes even a "coordinate system". All of those terms are pretty much correct.

As it turns out, the world isn't flat. What's more, it's not even round, but instead some weird elliptical-like shape.

Maps, on the other hand, are flat (unless you include those weird creases they get when people try and fold them the wrong way).

To confuse things even further, humans came up with a system of lines called "Latitude" and "Longitude". Lines of Latitude run around the globe, with a fixed(-ish) distance between them. As a result, they are actually parallel - and in fact some very boring people often call them "Parallels".

Lines of Longitude run up and down the global, and all start and end at the poles. As a result, the distance between them isn't constant, and they aren't parallel - although if you're only looking at a small frame of reference (eg, most maps) they will appear to be.

So the problem becomes, given a roughly roundish but actually warped elliptical planet, a series of artificial lines that are parallel(-ish) in one direction but not in another (even if they do appear to be), and a human race who prefers things to be flat (except for beer) - how do you actually reference any particular point on the planet?

Or to put it another way, how do you "project" those lines of latitude and longitude onto the almost-but-not-quite round Earth?

As it turns out, there's no end of answers. Most of them have silly names like ED50, ETRS89, GRS 80, NAD83, NAVD88, SRID, UTM, and you guessed it, WGS84!

Some of these systems use Latitude and Longitude, whilst some of them simply - like UTM - give up on the whole concept of the world round and pretend (at least in part) that it's flat - at which point putting straight lines on it becomes much easier.

WGS84 is one of the "world is round-ish" methods, and is by far the most common - if only for the fact that it's what the GPS in your car uses to work out how lost you are. It's also what you'll find used on most recent maps (but more on that below).

Many of the different projection schemes/datums will give very similar results for locations, but unless you're either visiting Santa at the north pole or visiting the Polar Bears at the south pole then they will vary slightly. Whilst most recent maps will use WGS84, many of them will also include details for other coordinate systems, like NAD83.

Now, what was the question? Ohh - that's right - where's the cave at 6413180-2059501?

The simple answer is, I have no idea what those numbers mean. Regardless of the Datum used, coordinates are usually expressed in degrees of latitude and longitude, not as mathematical equations like you have above. Attempting to convert the above into degrees could be done in three ways :

64.13180 degrees North, 20.59501 degrees West (west, due to the negative)

64 degrees, 13.180 minutes North, 20 degrees 59.501 minutes West (west, due to the negative)

64 degrees, 13 minutes, 18.0 seconds North, 20 degrees 59 minutes, 50.1seconds West (west, due to... well.. hopefully you've gotten the idea by now!)

(For those that have forgotten high-school math, there's 60 minutes in a degree. There are also 60 seconds in a minute, but I'm guessing you remembered that one!)

According to Google Maps, those put you here, here, or here - all of which are in Iceland. I do not, however, see any caves.

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The problem is, I assume he got it from the comment on this photo. And the map associated with the photo disagrees with at least the first option. – Mark Mayo Aug 14 '12 at 22:41
Correct, but it agrees perfectly with the 2nd option. Which I pretty much guessed when the 2nd option ended up being dead smack on a road - what are the odds? – Doc Aug 14 '12 at 22:43
In actual fact, the latter two seems pretty close.... – Mark Mayo Aug 14 '12 at 22:43
Thanks for explanation. I finally found a webpage that converts the coordinates into something google map undertands: boulter.com/gps/#64%2013.180%20-%2020%2059.501 – Karlth Aug 14 '12 at 22:48

Firstly, WGS84 is a considerably different format to regular Lat/Long coordinates.

Indeed, from a question on Stackoverflow, looking at the code to convert (if you were a programmer), it's quite a complex operation:

``````\$lon = (\$lon / 20037508.34) * 180;
\$lat = (\$lat / 20037508.34) * 180;
\$lat = 180/M_PI * (2 * atan(exp(\$lat * M_PI / 180)) - M_PI / 2);
``````

simply adding a decimal place isn't going to do it.

Running -2059501 through the LON calcuation, we get:

-18.5008

which certainly lines up with Iceland. However, I cannot manage to get any calculator here to do the second calculation - if someone else can help out?

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Using the formula above, the lat comes to 49.8085 (but this points to the middle of the ocean, so something's wrong with the formula) – Ansari Aug 14 '12 at 18:56
well the link to stackoverflow has several coders providing the same formula :/, including some who have pulled it directly from OpenLayers, so I suspect there's nothing wrong with the formula. Could be something wrong with the values though. – Mark Mayo Aug 14 '12 at 19:03
I briefly wondered if it was 64.13180, -20.59501 as that actually goes to Iceland, but after finding the cave photo online with their UGS84 coordinates, they have a map (Nokia maps) and it doesn't match up :/ – Mark Mayo Aug 14 '12 at 20:15