How to Convert Between Decimal Degrees and Degrees-Minutes-Seconds

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Every location on the earth’s surface can be represented by a point represented by a Latitude and Longitude. Most devices’ these days have a built in Global Positioning System (GPS) that can easily give you the coordinates of your current location. Most often you will see that the coordinates are given in terms of Degrees, Minutes, and Seconds (DMS format). Unfortunately that format is often cumbersome and difficult to work with, especially when performing computations or plotting points on a map or Geographic Information System (GIS). Knowing how to convert DMS coordinates to Decimal Degrees (DD) can improve your understanding of the arrangement and afford you the ability to easily work with the numbers.

Standard DMS values are written using a series of three different symbols followed by a directional indicator. An example of some coordinates that use this format are 111o23’14.8”W, 33o1’52.8”N. Sometimes the directional indicator is left off of the coordinates. In that case, the above example could be written as -111o23’14.8”, 33o1’52.8”. The negative sine denotes a westerly or southerly direction. The “Degrees” value in this example is 111 for the longitude and 33 for the latitude. The “Minutes” value in this example is 23 for the longitude and 1 for the latitude. And finally, the “Seconds” value in this example is 14.8 for the longitude and 52.8 for the latitude. In other words, the formatting is DDDoMM’SS.S”.

Another thing to keep in mind is that the longitudinal value (X-direction) is written first followed by the Latitude (Y-direction). This is the standard orientation when working with computers and GIS. If you’re using Google Earth or older GPS units, you may see the order of the numbers reversed.

Making the Conversion to Decimal Degrees

To make the complete conversion, you will be performing two separate calculations.

In the first step you convert the number of seconds in your coordinate to minutes. There are 60 seconds in every minute, so you will divide the number of seconds in your coordinate by 60 and add it to the number of minutes in your coordinate. Example:

If your coordinate is 45o22'38", divide 38 by 60 to get 0.6333. Add 0.6333 to 22 to get a result of 22.6333 minutes. The results for this example are 45o22.6333'. Note that your coordinate is now in the format of Degrees Decimal Minutes (DDM).

In the second step you will convert the number of minutes in your coordinate to degrees. Divide the number of minutes you have your coordinate (now in DDM format) by 60. Using the above example, take 22.6333 minutes and divide it by 60. The result is 0.3772 degrees. Add this value to the number of degrees you have in your coordinate to finish the conversion to Decimal Degrees (DD). In this example, the result is 45.3772o.

Congratulations! You have made the conversion. Converting back a DMS format is simply the reverse of this process. Subtract the 0.3772 off of 45.3772o and multiply by 60 instead of dividing it to get the amount of minutes. Then take the numerals after the decimal point in that result it multiply it by 60 to turn it into the number of seconds.

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