In this two-part edition of the Geospatial Frequently Asked Question (G-FAQ), I turn my attention to a broad topic we have visited before, that of coordinate systems, with a specific focus on two of the most commonly used, geographic and Universal Transverse Mercator (UTM). While UTM is increasingly used for regional mapping applications, this coordinate system is more complex to work with and can lead to mistaken locations if the proper information is not communicated, for instance zone number.
With this in mind, I address these core questions in this two-part G-FAQ series:
Is this UTM zone number important? How are UTM different than geographic (latitude and longitude) coordinates? When should I use each coordinate system?
Before we jump into this topic, let’s set the stage with a very brief discussion of projection. In the digital world of cartography, we typically simplify projection to refer to a combination of datum and coordinate system. A datum is a representation of the earth’s general shape upon which a geographic coordinate system is based, common ones are WGS84 and NAD83. A coordinate system is a gridded method to define positions on our planet. A geographic coordinate system is based on the angular distance of a point from the center of our planet. A projected coordinate system transforms geographic coordinates to a two-dimensional system that is more appropriate for display on a flat computer screen or paper map. Coordinate systems can be either global in their reach, such as geographic and UTM; or regional, such as state plane which we use in the United States. For a more detailed handling of this topic, please refer to the November 2012 G-FAQ.
The Geographic Coordinate System
Most of us are rather familiar with latitude and longitude (i.e. geographic coordinates) as they are commonly used on globes, wall maps and atlases. They are often written in decimal degrees format, such as 40.52 N, -103.17 W; or in degrees minutes seconds, 40° 31’ 0.2” N, 103° 10’ 0.2” W. The geographic coordinate system was adopted as the global system in 1871 at the first International Geographic Congress. While this adoption was still a matter of dispute for some years after the conference, eventually its recommendation of Greenwich, UK as the zero for longitude (i.e. the Prime Meridian) became convention on maps. By settling on a common global coordinate system, more accurate maps of the ocean, seas and land could be drafted which was an important asset for exploration and global shipping along established ocean routes.
Latitude and longitude represent a point’s position on our planet as its angular distance from the center of Earth. Latitude is the angular distance a point is north or south of the Equator with values ranging from 90° South to 90° North. Longitude is the angular distance a point is east or west of the Prime Meridian with values ranging from 180° East to 180° West. If you were to project every angular point out from the origin to a defined distance, you would create a sphere. As such, a geographic coordinate system is not a map projection by definition as latitude and longitude define a three-dimensional world. A map projection such as UTM is one that takes a 3D world and transforms the coordinates to a 2D flat world. When latitude and longitude is taken together with a datum, you can imagine how a geographic coordinate system is a 3D representation and then not a map projection.
The Universal Transverse Mercator Coordinate System
The concept of the transverse Mercator system can be dated to the 1700’s but it was not widely used until after World War II when it appeared on USGS topographic maps alongside ‘traditional’ latitude and longitude. UTM is a true map projection in that it takes 3D geographic coordinates and converts them to a flat, 2D world. This is achieved by placing a cylinder around the globe so that the open ends of the cylinder point east and west. When you do this, the cylinder touches the globe along a plane that runs north and south. It is where this plane touches the globe that a UTM zone is created, following an orientation from true polar north to true polar south. The globe is rotated 6 degrees longitude and the process is repeated. In this fashion, 60 UTM zones are created, each covering 6 longitude degrees, that are oriented in a north to south fashion (from 84° N to 80° S) across the face of the planet. As the zones follow the alignment of true polar north to south, UTM zones look a bit tilted when lain on top of the globe. Given that the plane defining each zone is close to the planet, when you transform coordinates to UTM distortion is minimized.
Each of the 60 UTM zones are 1,000,000 meters across so they do overlap slightly. They are numbered in succession starting from 180° W so that Zone 1 covers 180° W to 174° W, Zone 2 covers 174° W to 168° W and so forth. Within each of the zones, coordinates are written as a distance east and north of an arbitrary origin. As such, a set of UTM coordinates (i.e. easting, northing) could define a point on our globe at 60 different locations. Therefore, when you give someone UTM coordinates, be sure to also tell them the zone number (and ideally the datum)!
Easting and northing UTM values are determined in the following fashion:
- Easting – this UTM coordinate is akin to longitude. A central meridian is established in each UTM zone at 500,000 meters. While it is the central meridian from which the meters east (or west) a point is measured, it is established as a value of 500,000 (not 0 as we commonly do for an origin). This is done to avoid negative coordinates, so that the far eastern edge of a zone is 0 easting and the far western edge is 1,000,000 easting. For this reason, this coordinate is sometimes called a false easting.
- Northing – this UTM coordinate is akin to latitude. Northing is calculated as the distance (in meters) from the Equator. So in the Northern Hemisphere, it is easy to calculate this value. To avoid negative numbers, all northings in the Southern Hemisphere are calculated as meters from the Equator but 10,000,000 is added to the value; this is sometimes called a false northing.
So when you tell someone a set of UTM coordinates, not only do you to communicate the zone number, you need to tell them if the zone is north or south of the Equator. Just knowing a Zone number alone and an easting/northing defines two points on the globe. Here is an example of how to communicate UTM coordinates correctly:
NAD83 Datum; Zone 13N; 4,401,868 m N, 511,419 m E
This point is a location in Denver, Colorado.
Determining the UTM Zone Number of Geographic Coordinates
As a final note to this first part of our G-FAQ series on UTM versus geographic coordinates, let’s close with a way to determine the UTM zone number from geographic coordinates. The process is rather easy:
- Take your longitude coordinate in decimal degrees and add 180.
- Then divide by 6.
- Finally round up to the next highest whole number.
So for example, the UTM zone number for 39° W would be found through these steps:
- -39 + 180 = 141
- 141 / 6 = 23.5
- 23.5 rounds up to 24
So 39° W is in UTM zone number 24.
Do you have an idea for a future G-FAQ? If so, let me know by email at email@example.com.
Find Out More About This Topic Here
- Brown University – Coordinate Systems & The Role of Projections
- Idaho State University – Introduction to Topographic Maps
- National Park Service – Datums & Coordinate Systems Presentation
- Northern Arizona University – Coordinate Systems Workbook
- University of Wisconsin, Green Bay – The Universal Transverse Mercator System
Brock Adam McCarty