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Understanding GPS Co-ordinates

GPS Co-ordinates on the Dead Sea, Jordan for geoaching

Lowest Point on Earth - Dead Sea, Jordan.

If you want to know how to geocache properly then it's important to have a good understanding of how GPS co-ordinates work. This is especially useful when you are trying to solve puzzle caches.

Before we get going check out the photo on the right. I was geocaching near the Dead Sea in Jordan in November 2010.  I thought it would be interesting to see what the GPS altitude would be the lowest point on earth.  Look at the altitude... or whatever you call negative altitude.

BTW the geoaching app shown here is called Blackstar and works on Blackberries.  Unfortunately my BB died after it got wet after I got back.

But I digress...

Understanding GPS Co-ordinates

To understand how to geocache you'll need to become familiar with how co-ordinates work.

Lines of latitude

We start by cutting the world in half horizontally - this line is called the equator.

Horizontal lines that circle the earth are called lines of latitude.  Imagine that a line is drawn from the centre of the earth at angle to the horizontal.  This angle gives us degrees latitude above or below the equator.  So in the picture you can see N30, N50 N70 which are north of the equator, and S10, S30 which are south of the equator.

Globe showing grid co-ordinates

The earth with gridlines

So if your latitude co-ordinate has an "N" in front of it, then you are north of the equator, and if it has an "S" in front of it you are south of the equator. Going back to the Dead Sea, you can can see that we are located at 31 degrees to the north of the equator. And at the north pole, we would be 90 degrees above the equator.
If, as you move, your latitude numbers increase, in the northern hemisphere you would be heading further north, and in the southern hemisphere you would be heading further south.

Lines of longitude

The line that cuts the world in half vertically through Greenwich in London is called the prime meridian - as you can see in the picture.  Vertical lines that circle the earth are called lines of longitude.

Anything west of the prime meridian will have a "W" in the longitude, and anything to the east will have an "E" in the co-ordinate.   Going back to the Dead Sea, you can can see that we are located at 35 degrees to the east of the prime meridian.  If, as you move, your longitude numbers are increasing, and you have an "E" in front of your co-ordinate you would be heading further east, and if you have a "W" in the longitude,  you would be heading further west.

This is useful to know when you are solving puzzle caches.  For example if you are plotting numbers in Google Earth and see that the calculation takes you to the wrong location, do a whatif and see what happens if you increase either the latitude or longitude.  Increasing/decreasing the latitude number by itself, will move your point due north/south.  Alternatively, increasing/decreasing the longitude will move your point due east/west.

Degrees, minutes, seconds

Consider the co-ordinates shown on the Blackberry at the Dead Sea.

  • N 310 38.664
  • E 350 34.371

Since the world is circular (yes, I know it's almost a sphere, but work with me here!) it can be divided into 360 degrees.  However because, as we discussed above, cartographers divided the earth in to north/south, latitudes only go from from 0 to 90 degrees in the North or South.  Longitudes go from 0 to 180 East or West.

How far is one degree of Latitude?

You'll notice that latitudes are parallel lines wherever you are on earth. It means since the earth is almost a sphere, for geocaching purposes one degree of latitude is the same anywhere on earth. (OK the earth is slightly flat at the poles so latitude does vary but it's only a difference of about 1km between latitudes at the equator and the poles.)

A minute of latitude is 1/60th of a degree, and one second is 1/60th of a minute.

Geocaching uses Degrees, Minutes and Decimal minutes. You'll sometimes see it referred to as dd mm.mmm, for example in the setup menu of your GPS.  Some puzzle caches will use Decimal Degrees to be tricky and these are expressed as dd.mmmm.

So how far is one degree, minute and second?

  • 1° of Latitude (1/360th of the Earth's Polar circumference) is 110.5743 km (68.70768 miles)
  • 1' (1 minute) of Latitude (1/60th of 1°) is 1.8429 km (1.1451 miles)
  • 1" (1 second) of Latitude (1/3600th of 1°) is only 30.7151 m (100.771 feet)
  • 0.1" (1/10th second) of Latitude (1/36000th of 1°) is only 3.07151 m (10.0771 feet)

So for co-ordinates in the Degree/Decimal Minute format (dd  mm.mmm)...

  • If the co-ordinates change by 1 degree you would have moved 110.6 kilometres
  • If the co-ordinates change by 1 minute you would have moved 1844 metres
  • If the co-ordinates change by 0.1 minutes you would have moved 184 metres
  • If the co-ordinates change by .01 minutes you would have moved 18.4 metres
  • If the co-ordinates change by .001 minutes you would have moved 1.84 metres.

So that third decimal place in the co-ordinates doesn't make a lot of difference - very useful information when you're trying to solve a puzzle cache.  It's within the accuracy of your GPS.  So you don't need to solve that number to get within a search radius.  Even the second decimal place isn't that far away. It will get you somewhere pretty close.  This is one of the secrets of finding puzzle caches.

In the puzzle you know the degrees are going to be the same as where you are (unless you're near a degree confluence).  All you need to work out are the minutes and the first decimal point and you can see that you will be very close.  Just plot some numbers on Google Earth until you find somewhere that looks likely.

How far is one degree of Longitude?

Because lines of longitude converge as you get closer to the poles, the distance between longitudes  decreases as you move away from the equator and towards the poles. Therefore the distance depends on the latitude at which you are located.

For example at the equator, the distance between degree longitudes (say, between 150 and 151 degrees) is about 111.3 km.  However at 35 degrees latitude that distance is only 91.2 km.  Of course by the time you reach the pole it's zero.

Rather than digging out your old school scientific calculator, try this distance calculator here. It accepts various formats, so just use the usual geocaching dd mm.mmm.

Below is a table of distances between degree and minute longitudes that are calculated for latitudes from 0 to 90 degrees.

For example, if you are at 35 degrees latitude, then the distance between one degree longitudes is 91.2 km.  The difference between one minute of longitude is 1.52 km. The distances are also shown in statute miles.

So you can now calculate distances for decimal minutes in the same way as for latitudes above i.e. At 35 degree latitude 0.1 minutes is 152 metres, 0.01 minutes is 15 metres and 0.001 minutes is 1.5 metres.

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Converting from Decimal Degrees to Decimal Minutes

Sometimes, people use Decimal Degrees in their cache puzzles i.e. dd.mmmm You need to convert these co-ordinates into Decimal Minutes which is what is used for most geocaches.  Conversely you may want to convert from Decimal Minutes to Decimal Degrees.

It's actually very simple.

Since there are 60 minutes in a degree, to convert from Decimal Degrees to Minutes simply take the decimal part of the co-ordinate and multiply by 60. For example say the co-ordinate is S34.12345, multiply 60 x .12345 = 7.407.  So your co-ordinate would be S34 07.407.

To convert from Decimal Minutes to Degrees divide the minutes by 60.  So using our previous example, divide 7.407/60 = .12345.

It's the same process for either latitude or longitude co-ordinates.

Let me know if there is anything else that you would like to know about co-ordinates.

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