# Trying to figure out the length of a roll of material when i don't know the thickness

#### not007

##### New member
I have a roll of landscape fabric - material you put down under mulch to keep weeds out. But it doesn't work for me. So I'm selling it.

I did roll it out in my garage and measured it in 20' or so incremeents (it's about 150' long) but wanted to double check.

The only online calculators I could find (and there was a bunch) wanted inner and outer diameter.... and material thickness.

a) I don't know the thickness
b) seems that depending on how tightly rolled the item is, that will change the outer diameter / affect calculated result.

My thinking is that the number of wraps, OD and ID would work, but can't find a calculator for that. Any recommendations? Is that more of a calculus formula (I'm 57... I really don't remember calc other than the s shaped symbol? Or was that differential equations : )

But my thinking is that if you do it by hand you would do repeated circumference calculations using slightly larger diameters each time (and you'd be doing that x times where x= number of wraps?

Or you find the 'average diameter (or is it the mean? median?)', find the circumference there and multiply by the number of wraps? And the diameter i am thinking of is the midpoint of the material - the same length of material from there to the OD as from there to the ID. Would saying same area be a safe approximation? for a 5=od and 1.875 ID, I came up with diameter of 3.8 for same area above and below that diameter?

Is that another way to do it? Is 3.8" correct?

Should i roll it out on the driveway rather than use math : )

#### lev888

##### Senior Member
I have a roll of landscape fabric - material you put down under mulch to keep weeds out. But it doesn't work for me. So I'm selling it.

I did roll it out in my garage and measured it in 20' or so incremeents (it's about 150' long) but wanted to double check.

The only online calculators I could find (and there was a bunch) wanted inner and outer diameter.... and material thickness.

a) I don't know the thickness
b) seems that depending on how tightly rolled the item is, that will change the outer diameter / affect calculated result.

My thinking is that the number of wraps, OD and ID would work, but can't find a calculator for that. Any recommendations? Is that more of a calculus formula (I'm 57... I really don't remember calc other than the s shaped symbol? Or was that differential equations : )

But my thinking is that if you do it by hand you would do repeated circumference calculations using slightly larger diameters each time (and you'd be doing that x times where x= number of wraps?

Or you find the 'average diameter (or is it the mean? median?)', find the circumference there and multiply by the number of wraps? And the diameter i am thinking of is the midpoint of the material - the same length of material from there to the OD as from there to the ID. Would saying same area be a safe approximation? for a 5=od and 1.875 ID, I came up with diameter of 3.8 for same area above and below that diameter?

Is that another way to do it? Is 3.8" correct?

Should i roll it out on the driveway rather than use math : )
To estimate thickness:
Count the number of layers (n) in an inch.
Thickness = 1"/n.

#### Dr.Peterson

##### Elite Member
My thinking is that the number of wraps, OD and ID would work, but can't find a calculator for that. Any recommendations? Is that more of a calculus formula (I'm 57... I really don't remember calc other than the s shaped symbol? Or was that differential equations : )

But my thinking is that if you do it by hand you would do repeated circumference calculations using slightly larger diameters each time (and you'd be doing that x times where x= number of wraps?

Or you find the 'average diameter (or is it the mean? median?)', find the circumference there and multiply by the number of wraps? And the diameter i am thinking of is the midpoint of the material - the same length of material from there to the OD as from there to the ID. Would saying same area be a safe approximation? for a 5=od and 1.875 ID, I came up with diameter of 3.8 for same area above and below that diameter?

Is that another way to do it? Is 3.8" correct?
You can multiply pi times the average (mean) diameter, times the number of wraps: N*(ID + OD)/2.

If you used calculus (integral), or the sum of a series, you would get exactly the same result; this is because the circumference of each wrap increases linearly.

#### not007

##### New member
Wow! THANK YOU ALL for your time!

PLEASE read these with the smile on my face as I type this! NO malice / no intention to be sarcastic for the first two of you!!

LC - thanks, but that comes back to needing the thickness. and when dealing with a roll of a thin material, especially 1 that I unrolled then rolled back up : ), depending on how tight it get rewound, that will affect the OD. Goofy that so many pages require you to know thickness. Take a roll of paper towels, measure OD, unroll it. Roll it back up. Measure OD. Different numbers, right?!

lev - again, I'm trying to stay away from thickness... yeah, if I wound it tight I could do your way. I did the physical handling of it... trying to do the mental way now : )

Dr.Peterson - thanks. Yeah, OK, so I was on the right track? the average / mean IS the correct number to use for circumferance to multiply by number of layers? But just curious - That's not the right number if you wanted to figure the diameter that would give equal areas (area from that point to OD = area from that point to ID) , right? That's why I wasn't sure if that would give correct length.

Not to belabor this, but say there's 100 wraps. the (OD+ID)/2 would give you 50 wraps outside and 50 inside that diameter. But each of the 50 outside would have larger circumferences than the 50 inside / the lengths would be different. But like you said, sum of the series is equivalent to using the average? We're not trying to find the midpoint diameter with equal lengths inside / outside that diameter...

#### tkhunny

##### Moderator
Staff member
Not really a fan of estimating the thickness based on an inch of your wrapping or layering. This method relies on your ability to wrap in the same manner the manufacturer wrapped. Your personal efforts are unlikely to be anywhere near as tight as the manufacturer. Personally, I find it quite unlikely that if you purchased the materials legally, that there isn't a disclosure of the thickness somewhere. It MUST be in the manufacturing process and it is very likely to be printed on a box or other packaging somewhere. 6 mil is pretty common.

#### Dr.Peterson

##### Elite Member
Dr.Peterson - thanks. Yeah, OK, so I was on the right track? the average / mean IS the correct number to use for circumferance to multiply by number of layers? But just curious - That's not the right number if you wanted to figure the diameter that would give equal areas (area from that point to OD = area from that point to ID) , right? That's why I wasn't sure if that would give correct length.

Not to belabor this, but say there's 100 wraps. the (OD+ID)/2 would give you 50 wraps outside and 50 inside that diameter. But each of the 50 outside would have larger circumferences than the 50 inside / the lengths would be different. But like you said, sum of the series is equivalent to using the average? We're not trying to find the midpoint diameter with equal lengths inside / outside that diameter...
First, I think using thickness is fine, as long as it is the thickness as rolled, not as measured flat. That is, the thickness you use is (OD - ID)/(2N). The "official" thickness may, as you say, be practically irrelevant to the actual roll you yourself make.

But my formula has absolutely nothing to do with finding the point at which half the surface area has been rolled. That idea leads in entirely the wrong direction.

There are several ways to derive my formula.

One is the arithmetic series: the sum of the circumferences of the N layers is N times the average of the first and last terms (circumferences). If you relate this to one way to talk about sums of arithmetic series, you can say that the average of the nth layer from the inside and the nth layer from the outside is constant (equal to the length of the average layer), so the total length is just N times the average layer.

Another is to think about the volume of the rolled material: Total length times width times thickness is one way to measure it (unrolled); cross-sectional area ($$\displaystyle \pi R^2 - \pi r^2$$) times width is another (as rolled -- and we're defining thickness as rolled). This gives

$$\displaystyle Lt = \pi R^2 - \pi r^2$$,​

so

$$\displaystyle L = \frac{\pi(R^2 - r^2)}{t}$$.​

Since t = (R - r)/N, this gives

$$\displaystyle L = \frac{\pi(R + r)(R - r)N}{R - r}= \pi(R + r)N = \pi\frac{OD + ID}{2}N$$​

#### Romsek

##### Full Member
did you consider just weighing a known length of it and then weighing the entire bolt of fabric?

The ratio of the weights will be the same as the ratio of the length of the bolt and the test piece.

As long as there is no core of cardboard or something of unknown weight.

#### lev888

##### Senior Member
Not really a fan of estimating the thickness based on an inch of your wrapping or layering. This method relies on your ability to wrap in the same manner the manufacturer wrapped. Your personal efforts are unlikely to be anywhere near as tight as the manufacturer.
Not sure why I need to roll it as tight as the manufacturer. As long as I use measurements of _my_ roll it should produce correct results.

#### not007

##### New member
Thanks again!

Lev888 - if you roll it loose, then measuring the number of wraps in an inch of the radius would give less wraps = thicker material which isn't accurate. again, this is landscape fabric - thin fabric, not carpet. So fractions of an inch matter,

romsek - thanks. That would take cutting off a known length. Don't want to cut it up, but a good trick if you have extra piece : )

Dr- THANKS AGAIN!

TK - OOOOH! This thread took a sinister turn! : ) bootleg landscape fabric or fell off the truck.... or just bought it a while ago, threw away the wrapping with the specs.

#### lev888

##### Senior Member
Lev888 - if you roll it loose, then measuring the number of wraps in an inch of the radius would give less wraps = thicker material which isn't accurate. again, this is landscape fabric - thin fabric, not carpet. So fractions of an inch matter,
If you roll it loose it would correspondingly increase the outer diameter, no?

#### tkhunny

##### Moderator
Staff member
Not sure why I need to roll it as tight as the manufacturer. As long as I use measurements of _my_ roll it should produce correct results.
The difference is 1) measuring the thickness of the material (negligible gap), or 2) Measuring the average width of one lap (material + significant gap). If you're REALLY interested only in the length, then I would agree.

Calipers?

#### Subhotosh Khan

##### Super Moderator
Staff member
Calipers?
Pretty cheap these days and real handy for "approximately accurate" measurements.