Mathematical Conversion of Section, Township, and Range Notation to Cartesian Coordinates

Abstract

Section, township, and range notation provides sufficient information for accurate calculation of the coordinates of any location in an arbitrarily defined Cartesian coordinate system. First, such a set of calculations is derived; then, the results of these calculations are tested at 126 locations in Kansas. The mean absolute discrepancy for the x-coordinates (in Kansas) was found to be 0.447 mile and for the y-coordinates, 0.168 mile. Because of the complexity of the calculations involved and the number of figures that must be carried, the entire conversion from land grid notation to Cartesian coordinates was programmed in Fortran II for use on an IBM 1620 computer. A description of this program is also included.