In consultation with various state agencies, the National Geodetic Survey (NGS) devised the State Plane Coordinate System with several design objectives in mind. Chief among these were:

**Plane coordinates**for ease of use in calculations of distances and areas;**All positive values**to minimize calculation errors; and- A maximum error rate of
**1 part in 10,000.**

Plane coordinates specify positions in flat grids. Map projections are needed to transform latitude and longitude coordinates to plane coordinates. The designers did two things to minimize the inevitable distortion associated with map projections. First, they divided the U.S. into 124 relatively small zones. Second, they used slightly different map projection formulae for each zone. The curved, dashed red lines in the illustration below for Figure 2.27.1 represent the two standard parallels that pass through each zone. The latitudes of the standard lines are one of the parameters of the Lambert Conic Conformal projection that can be customized to minimize distortion within the zone.

Positions in any coordinate system are specified relative to an origin. **SPC zone origins are defined so as to ensure that every easting and northing in every zone are positive numbers.** As shown in the illustration below, SPC origins are positioned south of the counties included in each zone. The origins coincide with the central meridian of the map projection upon which each zone is based. The easting and northing values at the origins are not 0, 0. Instead, eastings are defined as positive values sufficiently large to ensure that every easting in the zone is also a positive number. The false origin of the Pennsylvania North zone, for instance, is defined as 600,000 meters East, 0 meters North. Origin eastings vary from zone to zone from 200,000 to 8,000,000 meters East.

### Try This!

**Investigating your local State Plane Coordinate System grid zone**

In this activity you will:

- read part of an authoritative manual on State Plane Coordinates;
- look up the designation of your local SPC zone (or a would-be zone if you are from a country other than the U.S.);
- investigate the parameters of the map projection upon which your local SPC zone is based; and
- use a web-based tool provided by the U.S. National Geodetic Survey to convert geographic coordinates to SPC.

#### 1. Read the introduction to the National Geodetic Survey manual *State Plane Coordinate System of 1983* by James E. Stem (1990).

Follow this link to download the manual in Portable Document Format (PDF). Read pages 1-13 (pages 11-23 of the PDF document). Also see Appendix A, beginning on p. 62 (73), which lists map projections and other parameters of each zone.

#### 2. Look up your local SPC zone.

- Visit the National Geodetic Survey's NGS Geodetic Toolkit. Note the various programs that NGS supports for the surveying and mapping community.
- Use the dropdown menu to navigate to the State Plane Coordinates tool.
- At the State Plane Coordinates page, follow the Interactive Conversions link labeled "Find Zone."
- Look up your local SPC zone (or adopted zone) by county or position.
- You might check the result using Rick King's list or the Stem (1990) manual you downloaded earlier.

#### 3. Look up the map projection and grid origin upon which your local SPC zone is based.

- Refer to the Stem (1990) manual you downloaded earlier. In particular, see Appendix A, pp. 63-72 (73-83). Upon which map projection is your local (or adopted) zone based?
- Note that the appendix reports a
**central meridian**and**scale factor**for each zone that is based upon a Transverse Mercator projection.**Standard parallels**are listed for zones based upon the Lambert Conformal Conic projection. In the Stem (1990) manual, "scale factor" is expressed in terms of maximum measurement error associated with each zone. - Appendix A also lists the SPC coordinates of each zone origin as well as its corresponding geographic coordinates.

#### 4. Use the NGS Toolkit to convert geographic coordinates to SPC coordinates.

- You'll need to know the geographic coordinates of a place of interest to complete this part of the activity. To look up the latitude and longitude associated with a U.S. place name, visit the USGS Geographic Names Information System. If you do not reside in the U.S., use the Getty Thesaurus of Geographic Names. Pay attention; be sure to choose the correct instance of the place name. Cities and towns are listed as "Populated Places" in the Geographic Names Information System and as "Inhabited Places" in the Getty Thesaurus.
- Return to the National Geodetic Survey's NGS Geodetic Toolkit.
- Use the dropdown menu to navigate to the State Plane Coordinates tool.
- At the State Plane Coordinates page, follow the Interactive Conversions link labeled "Latitude/Longitude -> SPC"
- Specify geographic (a.k.a. "geodetic") coordinates in degrees-minutes-seconds format. You do not need to show five places to the right of the decimal, as in the example illustrated above, but you do need to add a decimal point at the end of the DMS input values; the tool allows you to input a DMS value that is accurate to fractions of a second and so is programmed to expect the decimal point.
- A correct result will include a SPC Northing, Easting, zone, convergence (a correction factor for distance calculations that compensates for the tendency of meridians to converge toward the poles), and the scale factor