# Paper Math Explanation (imperial measurements)

**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.