Geographic coordinates are always in "degrees" but they can also include "minutes" and "seconds". This gives us a variety of different formats for reporting the coordinates and you'll see that different groups will use different formats. The format also impacts the precision of the data so it is critical to recognize and use them correctly.

Degrees, Minutes, and Seconds, or DMS, is the oldest format for geographic coordinates and you will still see this format in use on paper and even in movies where navigators will give their location in DMS.

- Latitude: 40° 51' 59" N
- Longitude: 124° 4' 58" W

Computers do not really work well with DMS coordinates and we really prefer the coordinates to be in Decimal Degrees or DD. This format allows us to perform standard decimal math operations on the coordinates. Even if you see DMS coordinates in a software package, the software will convert the coordinates to DD for calculations.

- Latitude: 40.866389°
- Longitude: -124.082778°

Degrees for DMS are divided into 60 minutes and then each minute is divided into 60 seconds. This is just like the hours on our clocks and goes back to the Babylonians who worked with a base 60 number system!

- Each degree contains 60 minutes
- Each minute contains 60 seconds

**DMS Formats**

One of the issues with DMS is that you will see them expressed in a variety of ways. This includes:

- 40° 31' 21" North by 105° 5' 39" West
- 40 31 21 N, 105 5 39 W
- 403121N, 1050539W
- 403121, 1050539

The last format is the most troublesome as when I first saw it, I thought the data was in UTM or another projected system. Since the data was off the coast of North America, I realized it was in DMS. I then quickly converted the data to DD.

Computer software will convert coordinates from DMS to DD on a regular basis without us even knowing it is happening. However, it's good to know the equation and I routinely see spreadsheets of data in DMS and I can quickly convert the data to DD because I know the following information.

First, recognize that:

- 60 minutes = one degree
- 60 seconds = one minute
- 3600 seconds = one degree

Using this, we can convert between DMS and DD with the equation:

**DD = Degrees + (Minutes/60) + (Seconds/3600)**

Converting between DD and DMS is now easy with the one addition that we need to remember that latitudes in the southern hemisphere are negative while longitudes in the western hemisphere (where most of the US is) are negative. Below is the conversion for a DMS coordinate near Arcata, California, in to DD.

Latitude = 40 + (51/60) + (59/3600) N = 40.866389°

Longitude = 124 + (4/60) + (58/3600) W = -124.082778°

We almost always need spatial data to be in Decimal Degrees in order to work with it in a computer. Here are some examples:

Name | Longitude | Latitude |
---|---|---|

Colorado State University | -105.082° | 40.5750° |

HSU | - 124.082778° | 40.866389° |

Paris | 2.2945° | 48.8582° |

South Pole | ? | -90° |

Bird's Nest (China) | 116.391° | 39.9915° |

The precision of geographic coordinates varies based on how they are formatted and regularly see coordinates in DMS with just the degrees without a decimal or minutes after them. The degrees are only precise to about 111 km so the coordinates are basically worthless. Use the information below to quickly compute how many digits you need to retain in DMS for the required precision:

- The Earth is about 40,000 km around
- 40,000 / 360 degrees ~ 111 km/degree
- 111 km/degree / 60 minutes/degree ~ 1.85 km/minute
- 1.85 km/degree / 60 seconds/minute ~ 0.03 km/second (30 meters/second)
- To maintain 1 meter accuracy, we need to keep two digits after the seconds decimal!

If we only keep the whole digits for the seconds (which is the most common approach), our data will only be precise to 30 meters. This may be enough for some applications but you would certainly not want to buy a parcel of land with 30 meters (90 feet) of error!

Precision in DD can be computed in an easier way.

- The Earth is about 40,000 km around
- 40,000 / 360 degrees ~ 111 km/degree or 111,000 m/degree
- To maintain 1 meter accuracy, we need to keep 5 digits after the decimal!

- Go to: http://geonames.usgs.gov/
- Search for a name
- What format are the coordinates in?
- What is the accuracy of the data?

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- Humboldt State University

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