By multiplying the zone number by 6 and subtracting 180, you may find the eastern limit of any UTM zone. The State Plane Coordinate System (SPCS) is unique to the United States and employs northing and easting coordinates. Let's look at the Easting of a point that is 146m east of the western grid line. That's what MOD does - it gives the remainder from an integer division. In the coordinate values, the Easting is x, Northing is y, and Elevation is z, so the x-component of the vector AB is given by x = 820462.32 - 819470.95 = 991.37, and similar computations for y and z produce the following values in feet: x y z AB 991.37 -68.96 -31.36 I've done this before, but the technique is at the office, I'm at home, and I'm too tired to do it right . Note: Krueger's n-series formulae are more accurate versions of Redfearn's formulae. The length becomes the hypotenuse of the triangle, the Azimuth is measured from north or south and the Delta N and Delta E are the legs of the triangle.