Computation of Scalefactor & Standard Parallel
For The Polar Stereographic Projection
In the pattern of most map projections, the polar stereographic projection comes with some parameters that must be supplied to fully specify the map projection and obtain grid coordinates. Two of these parameters are the central scale and the latitude of unity scale. Central scale (k_{0}) tells how a short (infinitesimal) curved segment at the Pole is reduced in size when represented on the map. It is a number between 0 and 1. The latitude of unity scale (φ_{1}) tells where on the ellipsoid a short (infinitesimal) curved segment is preserved in size when represented on the map. It is a number between –90 and 90 for latitude in degrees. This parameter is also called the “standard parallel”.

The two parameters are dependent. Either one may be chosen freely. After that, the other one is calculated from the first.

Many software packages which perform polar stereographic projection calculations allow either parameter to be the chosen userentered one. Not all these packages report the calculation of the other. The attached technical memo and sample programs do exactly that for both calculations − φ_{1} to k_{0} and k_{0} to φ_{1}.

Then, two programs are offered to do the calculations. An Excel spreadsheet is:
Calculator_for_polar_stereo_scale_v_std_parallel.xls

An executable file which runs in a DOS prompt window is:
Calculator_for_polar_stereo_scale_v_std_parallel.exe

The Clanguage source code for the above is contained in:
Calculator_for_polar_stereo_scale_v_std_parallel.c

C. Rollins
B. Akers
M. Factor
National GeospatialIntelligence Agency
December, 2011

Point of Contact: Coordinate Systems Analysis Team
phone (314) 6769124, DSN 8469124
coorsys@nga.mil
Document last modified