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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:
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
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 paper rolls and for other type of papers 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
Length of Paper in Meter:
58,590*M
W*G
Example: Let Net Weight of Roll (M) is 1100 lbs, Width of Roll (W) is 40" and Basis weight or GSM is 100g/m2.
Length of Paper in Feet = 58,590*1100/40*100 = 16,112 ft
Various Calculator available to calculate length of paper in a roll
http://www.casepaper.com/res_calculators.htm
http://www.beacongraphics.com/inkjet/roll-length-calculator.html
http://www.handymath.com/cgi-bin/rollen.cgi?submit=Entry