GPS Conversion Formula's

It has recently been brought to my attention that some of the GPS coordinates some computer programs use is the ddd/mm.mmm format. I knew about this but since I tend to do everything in the ddd/mm/ss.s format, I hadn't given it much thought. 
I would like to thank Sheldon for asking questions that inspired this page.
The latitude and longitude coordinates in the database on this website are simply entered 333338N  1175606W. This reads 33degrees/33minutes/38seconds North, 117degrees/56minutes/06seconds West. There are no decimal points. For that you are on your own.
You will see this coordinate system used exclusively throughout the database I have created on this site.
First a note: In many computer programs and on the internet, West longitude must be expressed as a negative (-), for example: (117/56/06.5) would be entered (-117/56/06.5).
Enough of that lets get to the calculations:

We will deal with three formats, ddd/mm/ss.s, ddd/mm.mmm and dd.ddddd.

I will use a practical location so this makes better sense to those who may be new to GPS.

We will start with a set location in Costa Mesa, California.
It has the GPS coordinates in the ddd/mm/ss.s format of  33/33/38.2N, 117/56/06.5W.
To convert this to ddd/mm.mmm you take the seconds (38.2) and divide it by 60        38.2/60=6366
round this off to three places and you have 33/33.636
Similarly 117/56/06.5 comes out to 117/56.108

To conmvert ddd/mm.mmm to ddd.ddddd, do as follows:
If you have ddd/mm/ss.s, first convert it to ddd/mm.mmm then take the mm.mmm (33.636) and divide that by 60 giving 56060. If necessary round to 5 decimal places we now would have 33.56060 and the 117/56.108 comes out to 117.93513.

To convert the other way:
Starting with 33.56060N, 117.93513W
Take the decimal and multiply it times 60   .56060*60=33.636 to give the ddd/mm.mmm format 33.636.
To get to the ddd/mm/ss.s format you must first get the dd/mm.mmm numbers. Take the decimal and multiply that times 60   636*60=38.160 (round to one decimal place) yielding 33.33.38.2
Do the same for the longitude numbers and your answers will come out:

33/33/38.2N 117/56/06.5W
33/33.636N  117/56.108W
33.56060N   117.93513W

Summary:

ddd/mm/ss.s to ddd/mm.mmm: ss.s/60=.mmm
ddd/mm.mmm to dd.ddddd: .mmm/60=.ddddd
dd.ddddd to ddd/mm.mmm: .ddddd*60=.mmm
ddd/mm.mmm to ddd/mm/ss.s: .mmm*60=ss.s
   
33/33/38.2N 117/56/06.5W = 33/33.636N  117/56.108W
33/33.636N  117/56.108W = 33.56060N   117.93513W

I hope that helps some of you.

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