Paper Length and Roll Weight Calculation

How to Calculate the Paper Length and Roll Weight?

Paper Length Calculation when Diameter of Roll & Paper Thickness is Known

If you know the outer diameter of the roll and the core on which paper is wound and the thickness of the paper, you can calculate the length of paper using following equations.

• Outer Roll Diameter :                           Do
• Outer Diameter of Core  :                   Di
• Thickness of Paper :                               t

English or US Units (Diameter in Inches and thickness in Point. Please note Point is 1/1000th of an Inch)

Length of Paper in Feet:            1000*3.1426*(Do^2 – Di^2) = 65.47*(Do^2 – Di^2)
                                                        (t*12*4)                                        t

Example: Let Outer Diameter of Roll (Do) is 40″, Outer Diameter of Core (Di) is 6.5″ and thickness is 8 Pt.

Length of Paper in Feet = 65.47*(40*40 – 6.5*6.5)/8 = 12,748 ft

Metric or ISO Units (Diameter in Centimetres and thickness in Micrometres)

Length of Paper in Meter:            1000*3.1426*(Do^2 – Di^2) = 78.56*(Do^2 – Di^2)
                                                        (t*10*4)                                        t

Example: Let Outer Diameter of Roll (Do) is 100 cm, Outer Diameter of Core (Di) is 16 cm and thickness is 200 micrometer.

Length of Paper in Meter = 78.56*(100*100 – 16*16)/200 = 3827 m

Open an Excel Sheet to calculate paper length

Please note that these equations assume that there is no air gap between adjacent paper layers hence this formulae should not be used for tissue and some other bulky paper rolls. Actual length may be less than the calculated length.

Paper Length Calculation when Weight of Roll & Paper Basis Weight is Known

If you know the net weight (Total weight – Core weight) of the roll and the Basis weight of the paper, you can calculate the length of paper using following equations.

• Net weight of Paper                            M
• Width of Roll                                       W
• Basis Weight of Paper                        G

Metric or ISO Units (Weight in Kgs, Width in cm  and Basis Weight in g/m2)

Length of Paper in Meter:    100,000*M
                                                        W*G   

Example: Let Net Weight of Roll (M) is 500 Kgs, Width of Roll (W) is 100 cm and Basis weight or GSM is 100g/m2.

Length of Paper in Meter = 100,000*500/100*100 = 5000 m

English or US Units (Weight in lbs, Width in Inches  and Basis Weight in lbs)

Easiest way is to convert lbs weight in to Basis weight or GSM

To use the Weight Conversion tool, please select a Type of Paper from the pull down menu, then enter a value in pounds and hit calculate. To reverse the calculation simply select “gsm²->lbs” and enter a gsm value.

lbs -> g/m²

g/m²->lbs

Type of Paper	BookBondNewsprintCoverIndexVellumTag
lbs
Grams/Square meter

 

Roll Length CalculatorNeed to know how much media is left on the roll? How much material is left? Here’s a tool that will help you estimate your rolled media… L = (((ROLL x ROLL) – (CORE x CORE)) x 3.14) / (48 x Thick) Diameter of the ROLL in inches: (i.e. 6.5) Diameter of the CORE in inches: (i.e. 2) Thickness of the STOCK in inches: (i.e. 0.003) roll length: feet.

Point to Paper Weight Conversion (This is true for typical uncoated paper and assume 12 Pt. thick is equivalent to 270 gsm)