Fiber coverage and mathematics in needlepoint

Of course, there is mathematics in the retail business of selling needlepoint.  After all, someone has to total the receipt.  But many people don't realize that the determination of how much fiber to purchase is calculated with mathematical formulas.  I have stitched inch squares of different fibers to see just how far one yard (or strand) of a fiber will go when stitching on 13-mesh or 18-mesh, etc.  It's nice to have a visual reminder as well as then having translated this into a mathematical formula.  I have also drawn rectangles showing 13.5 square inches (area covered by one skein of DMC perle 5) and 7.5 square inches (area covered by one skein of DMC perle 3).  Seeing the area definitely helps with the calculation of background fiber amounts.  People groan when I mention pi r squared, but that is the formula to determine the area of a circle. 

In kitting (that is, pulling the fibers) a canvas, the first order of business is to calculate the overall dimensions and square inches.  So it is 12x12 for a total of 144 square inches.  The background is how many inches?  I mentally let the design "fall" so that I can compute how much of the area is background.  Try it--the first time or two, it is confusing and difficult, but you soon become accustomed to visualizing how much space the design takes when it is compressed along the bottom of the canvas.

Rules of thumb for fiber coverage in basketweave:
          Perle 5 covers 13.5 square inches
          Perle 3 covers 7.5 square inches
          1 strand of Paternayan persian covers 1.15 square inches of 13 mesh; 1.25 of 12 mesh and 1.40 of
                           10mesh
          1 skein of silk 'n ivory covers more than 22 square inches
          1 skein of impressions, 1 ply, covers 18 square inches; 2 ply, 9 square inches
           a 10-meter spool of Kreinik covers almost 6 square inches  (I'm sure the 8 covers more than the
                      16 but not enough to really matter)