Projected coordinate systems

The surface of the earth is curved but maps are flat. To convert feature locations from the spherical earth to a flat map, the latitude and longitude coordinates from a geographic coordinate system must be converted, or projected, to planar coordinates.

 

Globe to map: geographic coordinates converted to planar coordinates

 

A map projection uses mathematical formulas to convert geographic coordinates on the spherical globe to planar coordinates on a flat map.

 

A projected coordinate system is a reference system for identifying locations and measuring features on a flat (map) surface. It consists of lines that intersect at right angles, forming a grid. Projected coordinate systems, which are based on Cartesian coordinates, have an origin, an x and a y axis, and a unit for measuring distance.

 

Map showing feature locations with x,y coordinates

 

Projected coordinate systems are based on Cartesian coordinates which use a grid. Feature locations are measured using x and y coordinate values from the point of origin.

 

The origin of the projected coordinate system (0,0) commonly coincides with the center of the map. This means that x and y coordinate values will be positive only in one quadrant of the map (the upper right). On published maps, however, it is desirable to have all the coordinate values be positive numbers.

To offset this problem, mapmakers add two numbers to each x and y value. The numbers are big enough to ensure that all coordinate values, at least in the area of interest, are positive values. The number added to the x coordinate is called a false easting. The number added to the y coordinate is called a false northing.

 

Map with false easting and false northing values

 

By adding a large number to each x and y value, all coordinate values on the map are positive. In the graphic above, a false easting value of 7,000,000 was added to each x coordinate. A false northing value of 2,000,000 was added to each y coordinate.