# How to calculate remaining volume of a wire spool

There are a bunch of rolls of 3d filament at my library in various degrees of emptiness/fullness. When I pick one I need to know that it likely has enough remaining for my print job.

How can I calculate the (approximate) volume remaining of a spooled wire, given the diameter of the core/center of the spool (nonusable area) the original diameter of the spool when it was full, and the diameter of the material currently remaining on the spool?

If I'm looking for a percentile answer then I doubt the width of the spool comes into play, but they're aboue 2.5 inches wide.

If the core is 4 inches and there's currently 6 of material where there were originally 8, I know that it's not 50% empty, because each layer is larger than the next.

The filament is 1.75mm, but it might be easier to assume that its infinitely thin, or a liquid somehow evenly attracted to the spool core.

I do imagine the diameter of the filament and the way it's packed (square, or hexagonal/staggered) might impact a little do if I was trying to calculate length, but I'm hoping not for volume.

I found this answer: https://3dprinting.stackexchange.com/a/19038 but I put it into a spreadsheet and it doesn't look right at all:

PctRemaining=(100*((CurrentDiameter-EmptyDiameter)/(FullDiameter-EmptyDiameter)))^2

So what's the right way to solve this?

## 2 answers

The relative volumes of cylinders with the same height are proportional to the square of their diameter. Hopefully you can see this is true without further explanation.

The relative volume of wire on a full spool is therefore

D^{2} - D_{empty}^{2}

Now take the ratio of the current to the full wire volume using the above formula:

Fullness = (D_{curr}^{2} - D_{empty}^{2}) / (D_{full}^{2} - D_{empty}^{2})

Note that D_{full} and D_{empty} are constants for your purposes. To get remaining length of wire from the fullness fraction only requires another constant. During use, you therefore only need to perform the calculation:

WireLength = (D^{2} - K_{1})K_{2}

You can write K_{1} and K_{2} on each spool when you receive it full.

After I wrote up the question, I think the answer just hit me.

Calculate the area of three circles: (was going to say cylindars, but I don't think that axis matters) a) the minimum/empty diameter b) the maximum/full diameter c) the current media diameter

Then: b-a = the starting area of media c-a = current area of media

current area / starting area = % remaining.

For an 8 inch diameter spool with a 4 inch core:

The smaller the core, the more pronounced the curve. If the core is 1000 inches, then it looks almost straight, as I'd expect.

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