There are two sceneries
The most common, you know the weight of the roll. It is straightforward, since you most possibly know the width, and weight per area.
The special case, you know the length, but don’t know the final diameter of your roll, or you know the diameter but would like to know the length.
For this second case, for the
1st turn, you will have r1=r0 and S1= 2 x pi x r0
2nd turn r2=r0+e and S2 = 2 x pi x (r0+e)
i turn ri=r0+(i-1) Si = 2 x pi x (r0+(i-1) x e)
n turn rn=r0+(n-1)= rfinal Sn= 2 x pi x (r0+(i-1) x e)
Where r0 is the initial radius (core radius) or core diameter/ 2
e is the thickness of the sheet
And n is the total turns.
If you don’t know n you can divide (rfinal-r0)/e
Adding the S between I=1 and N
Stot = n x (2 x pi x r0) + e x 2 x pi x (Sum (i=1 to n) (i-1))
Stot = n x (2 x pi x r0) + e x 2 x pi x

(n-1)/2
Stot = n x (2 x pi x r0) + e x 2 x pi x

(n-1)/2
Stot = n x 2 x pi x (r0 + e (n-1)/2))
The formula is easily seen as a stack of n sheets, with the shorter with a length of 2 x pi x r0 and the longest with a length of s x pi x r final. The length would be the mean length multiplied by the amount of sheets.
sancat