Lenght of Material on a core.?

Question

I need to know the mathematical formula to calculate the feet i have left on a roll of paper. if someone can post it i would be very greatful.

Answer 1

You have to know the radius of the core (rc), the radius of the whole roll (rr), and the thickness of the paper (T). The number of turns N is the thickness of the wound paper layer divided by the paper thickness:
N = (rr - rc) / T
and the length of the paper is N times the average circumference of the wound paper layer:
L = N * 2 * pi * (rr + rc) / 2
Combining, the length of the paper is
L = pi * (rr + rc) * (rr - rc) / T
The trick here is to measure the paper thickness T accurately. The pressure of a micrometer may not duplicate the pressure the paper experiences in the wound layer. If accuracy is important enough, you can obtain T indirectly from a new roll whose paper length L is known. In this case you'd measure rr and rc on the new roll and use the previous equation, rearranged as:
T = pi * (rr + rc) * (rr - rc) / L