Paper Math Explanation (imperial measurements) (vers.6)

TERMS & DEFINITIONS

Basis Weight (pounds): The weight of a ream, measured in pounds. of the basic size.
Purchase Width (inches): Custom/used actual width
Purchase Length (inches): Custom/used actual length
Basic Width (inches): The standard width from which the basis weight of a given grade of paper is determined
Basic Length (inches): The standard length from which the basis weight of a given grade of paper is determined
Basic Size (inches): The standard sheet size from which the basis weight of a given grade of paper is determined
Ream: 500 sheets of paper cut to a given standard size for a particular grade.
Ream Weight (pounds): The weight of 500 sheets of paper.
M-weight (pounds): The weight of 1,000 sheets of paper (or two reams).

For reference, common basic types and sizes are as follows:

Stock Type Width x Height (mm) Width x Height (in)

Bond 558.8 x 431.8 mm 22.0 x 17.0 in
Book 965.2 x 635.0 mm 38.0 x 25.0 in
Cover 660.4 x 508.0 mm 26.0 x 20.0 in
Index 774.7 x 647.7 mm 30.5 x 25.5 in
Newsprint 914.4 x 609.6 mm 36.0 x 24.0 in
Offset 965.2 x 635.0 mm 38.0 x 25.0 in
Text 965.2 x 635.0 mm 38.0 x 25.0 in
Tissue 914.4 x 609.6 mm 36.0 x 24.0 in

Example 1 - per 100 pound pricing ( CWT )

Basis Weight x Purchase Width X Purchase Length = X
Basis Width X Basis Length = Y

X / Y = actual weight of 1 ream ( 500 sheets )

The purchased sizes are multiplied with the basis weight, then everything divided by the basis size so we find out the actual weight of 1 real (500 sheets).

70 lb Text X 23 Inch X 35 Inch = 56350
25 Inch x 38 Inch = 950
56350 / 950 = 59.31578947
Ream weight X 2 = Mweight 118.631789

If the price is based on 100 lbs ( cwt ) then:

Cost per 100 lb x actual weight of a ream / 100 

for example

$55.00 x 59.31578947 / 100 = $32.62 for 500 sheets of 23 x 35 70 lb 

text stock so,

Weight = 59.31578947
Cost = $32.62
Square Area = 500 sheets X 23 Inch X 35 Inch = 402,500 square inches

Then: 

Weight per square inch = 59.31578947 / 402,500 = 0.000147368421052632 lbs
Cost per square inch is $32.62 / 402,5000 = $ 0.0000810434782608696

Example 2 - per 1000 sheet pricing

Basis Weight x Purchase Width X Purchase Length = X
Basis Width X Basis Length = Y
X / Y = actual weight of 1 ream ( 500 sheets )

70 lb Text X 23 Inch X 35 Inch = 56350
25 Inch x 38 Inch = 950
56350 / 950 = 59.31578947
Ream weight X 2 = Mweight 118.631789

If the price is based on 1000 sheet then:

Cost per 1000 sheet is in $

Weight = 118.631789 pounds
Cost = $65.24
Square Area = 1000 sheets X 23 Inch X 35 Inch = 805,000 square inches

Then 

Weight per square inch = 118.631789 / 805,000 = 0.000147368681987578 lbs
Cost per square inch is $65.24 / 805,000 = $ 0.0000810434782608696

Note there is a weight variance in the above around the tenth decimal place between the two examples.