A mathematical framework that flattens the three-dimensional, curved surface of the Earth into a two-dimensional plane. While a Geographic Coordinate System (GCS) defines locations on a sphere using angles (latitude and longitude), a PCS defines locations using linear measurements (easting and northing) on a flat grid.
Because it is impossible to flatten a sphere without stretching or tearing it, every PCS introduces some form of distortion. The goal of a specific PCS is to minimize distortion for a particular geographic area or for a specific property, such as area or distance.
Core Components of a PCS
A PCS is not a standalone system; it is built upon several layers of information:
1. Geographic Coordinate System (GCS)
Every PCS must be based on a GCS, which includes a datum (such as WGS 84) and an ellipsoid. This provides the 3D model that is being flattened.
2. Map Projection
The mathematical algorithm used to transform 3D coordinates into 2D coordinates. Common types include:
- Cylindrical: Imagine wrapping paper around the equator (e.g., Mercator).
- Conical: Imagine placing a paper cone over the poles (e.g., Lambert Conformal Conic).
- Planar: Imagine placing a flat sheet of paper against a single point on the globe (e.g., an Azimuthal Projection).
3. Linear Units
Unlike GCS, which uses degrees, a PCS uses constant units of measurement—most commonly meters or feet. This makes it possible to calculate area, perimeter, and distance accurately.
The Four Properties of Distortion
When choosing a PCS, analysts must decide which geographic property is most important to preserve, as a flat map cannot keep all four perfect:
- Area: Preserved by Equal-Area projections. Essential for land-use mapping and thematic maps.
- Shape: Preserved by Conformal projections. Crucial for navigation and topographic mapping.
- Distance: Preserved by Equidistant projections. Used for seismic mapping and airline routes.
- Direction: Preserved by Azimuthal projections. Important for sea and air navigation.
Common Projected Systems
| System Name | Type | Best Used For |
| UTM (Universal Transverse Mercator) | Cylindrical | Regional mapping and high-accuracy engineering. |
| State Plane Coordinate System (SPCS) | Various | Highly localized surveying within the United States. |
| Web Mercator (EPSG:3857) | Cylindrical | Web maps like Google Maps and OpenStreetMap. |
| Albers Equal-Area Conic | Conic | National-scale maps of the US to preserve land area. |
Why Use a PCS?
While GCS is excellent for global data storage, it is problematic for analysis. Because degrees of longitude vary in width depending on your distance from the equator, calculating the area of a polygon in square degrees is not consistent. A PCS provides a stable, uniform grid where:
- 1 + 1 always equals 2 in terms of distance.
- Spatial operations such as Buffer and Intersect yield mathematically reliable results.
- Map features look natural to the human eye within their intended region.