How much paper is left on the roll??

Here is a useful way to calculate how much paper is left on a partial or butt roll. All you need is a tape measure and our generation’s seventh grade algebra, which is third grade algebra today. If the thought of algebra makes you cringe, just skip the next few paragraphs and look for the words “If you decided to skip…”

For you braver souls, you will need to recall these concepts.

The diameter of a circle is the length of a straight line that runs from edge to edge and passes through the exact center. The circumference of a circle is the length around the outside edge around the circle. Pi (π) is that magical number of 3.14159 that some genius tells us we need to use when working with circles. Pi was calculated, in fact, as the result of the circumference divided by the diameter. Therefore, if you know pi times the diameter (also shown as D, pronounced pie-dee), you’ll get the circumference. That’s it for the theory.

All you’ll need to know is the diameter of the roll, the diameter at the core and the caliper to figure out how many lineal inches there are on the roll.

Example: Roll diameter (RD) = 51 inches, core diameter (CD) = 12 inches and the caliper is .018.

Roll circumference = 3.14159 x 51 = 160.2 lineal inches.

Core circumference = 3.14159 x 12 = 37.7 lineal inches.

That means that the longest lap around the roll is 160.2 inches long and the shortest lap around the roll is 37.7 inches long. The average lap is almost exactly 99 inches (160.2 + 37.7) ÷ 2). So now that we know how long the average lap is all we need to know is how many laps there are and we’ll be able to calculate the total number of lineal inches on the roll.

The height of any pile of paper in inches divided by the caliper is equal to the number of sheets in the pile. (See Fig. 2) So, one inch of .018 paperboard has 56 sheets in it (1 ÷ .018 = 56). In our example, if we were to cut the roll at the same place and make a pile of the laps that fell off, the pile would be 19.5 inches high (51RD-12CD) ÷ 2).

Why divided by two? Because you have the same amount of paper on each side of the diameter when the roll is in roll form but isn’t really there when you lay the sheets flat. This should make sense after you think about it. If not, please send me an email or give me a call.

That pile would have 1083 laps (19.5 ÷ .018) of many lengths as described above whose average length is 99 inches.

Well, if the average length is 99 inches and there are 1083 laps then the total inches is 107,217 (99 x 1083) lineal inches or 8,935 lineal feet. Once you know the lineal feet on the roll you can determine total roll square feet by multiplying the lineal feet times the roll width in feet.

If your roll width is 30.0 inches (2.5 feet), in our example you have 22,337 square feet (8935 x 2.5) on the roll or 22.3 MSF (thousand square feet).

If you decided to skip ahead, start reading here. You can forget all the above mumbo jumbo and go by the following formulas to get the lineal inches on the roll:

A = roll diameter x 3.14519

B = core diameter x 3.14519

C = (A + B) ÷ 2

D= (diameter – core diameter)

÷ 2 ÷ caliper

Lineal inches on the roll = C x D

If you have trouble with the math, just ask any 10-year old.