Tuesday, June 22, 2010

GPS Maps 102: Coordinate Systems and Conversions

[This post is part two in a multi-part series about understanding the GPS system and its coordinate grid.]

Ok, you should remember from the last time we spoke that there are "Parallels of Longitude" drawn east-west [equator] and "Meridians of Latitude" drawn north-south [Greenwich Prime Meridian] and where any of them cross into each other is where you are! [or want to be]

But, the main thing is, that those coordinates are radial angles expressed in degrees or fractions thereof and have nothing to do with actual distances – except probably tangentially (speaking linguistically not geometrically).

Additionally, thousands of years of "trial and error" efforts have left us with several, sometimes very confusing, alternate methods of recording locations and often the need to convert from one old system to the other.

Conversion Between Systems

It may be cumbersome, but it is not impossible for a rider to convert from the Decimal system into the Sexagesimal system [of or relating to or reckoning in sixtieths]; or, as commonly called the DMS (Degrees/Minutes/Seconds) system – again, they are NOT the same.

The first is the location's degrees expressed in a base-10 decimal fraction with usually 6 or more significant figures to the right of the decimal place.  The second is the location expressed in Degrees, 60ths of a degree (minutes) and 3,600ths of a degree (seconds).

For example Kurt's Grotto Petroglyphs: 36.430341; -114.223328 in Decimal Degree representation can be converted to DMS by first taking the number to the left of the decimal place and calling them "Degrees." 36 (lat) and -114 (lon) respectively.

Then multiply the remainder by 60 and get the minutes with a decimal fraction. You now have the coordinates: N (because it was positive) 36° 25.820'; W (because it was negative) 114° 13.400'. You can stop there and you will have the coordinates in the "Degrees and Decimal Minutes" coordinate system, a junky system fortunately rarely used.

Or, take the remaining fraction and multiply yet again by 60 to get seconds with a decimal fraction; and Finally, obtain the DMS values: N 36° 25' 49.227"; W 114° 13' 23.9802".

Converting the other way around (DMS to Decimal Degrees) merely involves division instead of multiplication.

Degrees + ((minutes + (seconds ÷ 60)) ÷ 60) = Decimal Degree Coordinate.

Lets take the DMS coordinates for "The Wave" in southern Utah and Arizona, 36° 59' 44.3148"; -112° 0' 21.4986", which I've borrowed from an upcoming trail map for this illustration.

To follow the above formula:

Seconds ÷ 60 = 0.73858 and 0.35831 decimal seconds,
Add the minutes = 59.73858 and 0.35831,
Minutes ÷ 60 = 0.995643 and 0.00597183333 decimal minutes,
Add the degrees to get Decimal Degrees: 36.995643; -112.00597183333


The Decimal Degree system is the ONLY system which is used by any of the software on the web; or, by any of our GPS systems. The base-10 system is the only one computers understand.

To be easy on us, our machines often do us a favor and render the displays using the above given formulas before they show it to us. They also must do the reverse conversion after we type in coordinates in any other system.

Be careful doing too much rounding of numbers because, as we will eventually see before finishing this series, 0.000001 degree equals a substantial error; especially when trying to find the entrance to a cave or to avoid a desert sink hole.

And accuracy, along with the striving for it, has been the biggest pain in the backside for adventurers, navigators and scientists ever since people wanted to "get there from here."

We've got a few more things to cover before this series ends such as "just how did they do it before satellites," "does the squashing of the earth make a difference," "what is all the UTM Easting and Northing stuff," and "does any of this have anything to do with just how far it is from here?"

Learn A Little More

There are many sites on the web which have conversion forms to help you convert from one system to the other. I'll list several for you to try. In my opinion there is one clear "winner" who does it best and most accurately.


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