The State Plane Coordinate System

Figure 1. The zones used in the State Plane Coordinate System (SPCS). This image is clickable; click on any state to see a more detailed map of the SPCS zones in that state.

In some parts of the United States, the State Plane coordinate system (which is alternatively abbreviated as SPS or SPCS) is extremely popular among state and local governments. Its popularity is primarily due to its accuracy -- in terms of linear measurements, it's four times as accurate as the Universal Transverse Mercator (UTM) system. However, it achieves this accuracy through the use of relatively small zones, and these small zones can be quite a problem in mapping projects covering larger areas. Because of this limitation, the state plane system has never really caught on for regional or national mapping tasks.

The history of the state plane coordinate system goes back to sometime around 1930, when an engineer from the North Carolina state government (there are conflicting stores about exactly who this engineer was, and what state agency he worked for) approached the U.S. Coast and Geodetic Survey office. The U.S. Coast and Geodetic Survey has since been split into two agencies, the Office of Coast Survey (OCS) and the National Geodetic Survey (NGS), both of which are located within the National Oceanic and Atmospheric Administration (NOAA). The Office of Coast Survey has primary responsibility for developing maritime charts and other navigational aids for U.S. seaports, while the National Geodetic Survey is responsible (along with the U.S. Geological Survey), for creating and maintaining survey control points for lands within (or controlled by) the United States (survey control points are things like the monuments used to identify the initial points and secondary points used in datums)1. The Coast and Geodetic Survey is the agency founded by Ferdinand Hassler, the same guy who came up with the first complete description of the polyconic projection.

At any rate, sometime around 1930, an engineer from the North Carolina state government approached the Coast and Geodetic Survey Office and inquired about the possibility of using simple techniques to survey the entire state. The simple techniques that the engineer wanted to use ignore the curvature of the Earth and instead assume the Earth's surface is simply a flat plane (for this reason, these simple techniques are called plane surveying techniques). Plane surveying techniques use Cartesian coordinates, and require nothing more than simple Euclidean geometry (I've always had the impression that this engineer was either lousy with math or just plane lazy, but I'm probably being unfair).

If you've gone through the previous learning guides, you know that it isn't possible to flatten the curved surface of the Earth into a flat plane without distorting the surface in one way or another. What the engineer was requesting was a spatial coordinate system with no distortion, and its mathematically impossible to create such a system. However, the North Carolina engineer evidently wasn't aware of this fact, so my guess is that he left the Coast and Geodetic Survey office rather disappointed that fateful day. Nonetheless, the engineer's visit led to a cooperative venture between the Coast and Geodetic Survey and the North Carolina state government, and efforts to build a North Carolina spatial coordinate system with minimal distortion was started. In 1933 this cooperative venture produced the North Carolina Coordinate System. In less that 12 months, the North Carolina system had been copied into all of the remaining states, and the State Plane coordinate system was born.

In its modern form, the state plane coordinate system covers all 50 of the United States, but it does not extend beyond the borders of the U.S. The system is designed to have a maximum linear error of 1 in 10,000. This means that if you use state plane coordinates to measure a line as being 10,000 units in length (you can use any measurement units you like -- feet, meters, miles, cubits -- it doesn't mater), you may be off by as much as one unit (i.e., the line might be anywhere from 9,999 to 10,001 units in length). This is four times as accurate as the UTM system, whose maximum linear error is 1 in 2,500, which, when you multiply both sides by four, translates into a maximum error of 4 in 10,000.

Like the UTM system, the state plane system is based on zones. However, while the boundaries of UTM zones follow lines of latitude and longitude, state plane zones generally follow political boundaries. First, no state plane zone spans more than one state, so all boundaries between states are also boundaries between state plane zone. Furthermore, given the state plane system's desired level of accuracy, many of the larger states are too big for a single state plane zone. These large states are divided into multiple zone (Figure 1). Generally, the boundaries between state plane zone within a state follow county lines. The only exception to this county-boundary rule occurs in Alaska; the counties in Alaska are so huge that it isn't possible to use county boundaries to define zone boundaries and still maintain the state plane system's desired 1 in 10,000 level of accuracy. Thus, in Alaska, state plane zones fall back into the UTM pattern of following lines of latitude and longitude. All totaled, the state plane coordinate system uses about 120 zones to cover the entire United States.

State plane zones whose long axis run north-to-south (e.g., Idaho West, Illinois East, or New Mexico Central -- click on a few states in Figure 1 to see more examples) are mapped using a Transverse Mercator projection, but unlike the Transverse Mercator projection used in the UTM system, the State Plane system uses a Transverse Mercator projection that is tangent, not secant. State plane zones whose long axis runs east-to-west (e.g., Texas Central, Washington South, and Pennsylvania South -- click on a few states in Figure 1 to see more examples) are mapped using a Lambert Conformal projection. In either case, the projection's central meridian is generally run down the approximate center of the zone. Almost all state plane zones are mapped using the Clarke 1866 spheroid. The only exception to this rule involves Michigan. In Michigan, state plane zones are mapped using the rarely encountered "Michigan spheroid", whose surface is generally about 800 feet higher than the Clarke 1866 spheroid.

Once a zone is mapped, a Cartesian coordinate system is created for the zone by establishing an origin some distance (usually, but not always, 2,000,000 feet) to the west of the zone's central meridian and some distance (there is no standard; each zone uses its own unique distance) to the south of the zone's southernmost point (Figure 2). This ensures that all coordinates within the zone will be positive. The X-axis running through this origin runs east-west, and the Y-axis runs north-south. Distances from the origin are generally measured in feet, and just as is the case with the UTM system, X distances are typically called eastings (because they measure distances east of the origin) and Y distances are typically called northings (because they measure distances north of the origin).

Figure 2. The geometry of establishing an origin for the Colorado North State Plane Coordinate System zone.

1I would like to thank Mr. Dave Minkel of NOAA for setting me straight regarding the history of the U.S. Coast and Geodetic Survey.