When I look at a majestic tree, I see a huge pile of toilet paper rolls.
Don’t believe me? Well, you got me, but there are people that see trees exactly that way, since – big secret – trees are ground up to make toilet paper. So the question that I was researching (and having a darned hard time answering) was just how many toilet paper rolls can one tree make?
For instance, Wikipedia, that hallowed source all all things somewhat accurate, states a tree produced 100 pounds of toilet paper rolls, and then linked to a reference that in turn linked to another and so on until a dead end. Logically, however, I can carry 200 rolls (100 pounds at about 1/2 pound a roll), but I can’t carry one tree (maybe a wee little tree). So something was off.
The problem is hard for a very simple reason: Trees come in all different sizes. So skip trees, and go straight to wood. In theory, the math is somewhat simple: Wood weighs about 20-40 pounds per cubic foot, depending on species. A toilet paper roll is about 1/2 pound, so one cubic foot of wood is good for about 40-80 rolls. Done and done.
Now this is a ‘back of envelope’ calculation. Moisture can affect the weight, but dried wood and paper seem ‘about’ the same, moisture wise. As this site points out, the difference between fresh wood and 20% moisture air dried wood is about 50% by weight, so we are in the ball park with our calculations.
But this still leaves a problem – how much does a whole tree make?
Well, each tree is different: Sizes among species (and individual trees) differ, so we can’t get much closer than that. However, mathematically, we can get an eyeball estimate, good for guessing how much a typical tree makes when on a walk in the woods.
For this, let’s estimate a tree is 40 feet high, and that it’s 18 inches wide at the ground (1.5 feet diameter, or 0.75 radius), tapering uniformly to the top. This ‘perfect’ tree is then a perfect cone, and gets its volume with this formula
Volume = ( pi * radius * radius * h ) / 3
= ( 3.1415 * 0.75ft * 0.75ft * 40ft ) / 3
= 23.56 cubic feet
So that 40 foot tree is about 24 cubic feet, which at 20-40 pounds/cubic foot makes it 480-960 pounds, and that ends up being 960-1,920 rolls. Of course, with the species, you could figure out the density, and get a more precise value – fir and pine are both around 30 lb/ft^3, so you’d be smack dab in the middle there, at 1,440 rolls. Isn’t math fun?
Of course, I’ve never seen a perfectly conical tree, and neither have you – most stay a certain width until almost at the top, then taper suddenly. To see the difference with our mythical conical tree, imagine it has a sibling, which is uniformly 18 inches from root to top, and also 40 feet tall. Now the volume is:
Volume = pi * radius * radius * h
= 3.1415 * 0.75ft * 0.75ft * 40ft
= 70.68 cubic feet
Not coincidentally, three times the volume of the conical trunk (compare the formulas). And the estimate triples, to about 4,500 rolls per tree.
As you can see, there’s good reason people have trouble figuring out how much of a tree makes how many rolls, and why it’s so hard to get solid figures. The math is here so you can do your own estimate, rather than rely on a number someone just posted (or perhaps inserted into Wikipedia!) And while there is quite a lot of wiggle room, roughly speaking, a solid 40 foot tree 18 inches wide can produce about 3,000-6,000 rolls, with about 4,500 for pine or fir.
Of course, I’m interested in checking this, and in fact, as I was researching this, I came across a paper site which referred to an old estimate – in this case, using 40 foot trees 6-8 inches wide. If we average to 7 inches (a radius of 0.29 feet) then the volume becomes 10.68 cubic feet per tree. In their calculations, one ton of paper comes from 12 of these trees, for a grand total of 15.6 pounds of finished paper per cubic foot of wood (about 30 rolls), or 166 pounds/332 rolls per tree – at least from these calculations. And since our trees were roughly 7x as big (70.68 versus 10.68 cubic feet), then we should have an estimate of 1,102 rolls per tree – ‘our’ tree. Since our estimate is much higher (at 3-6,000), this means that the calculations are missing something, such as the amount of waste in the wood making process.
So, is it 1,000? 2,000? 6,000? Personally, I would aim lower since waste in the paper making process was not discussed in this estimate (and I expect there is a lot of waste). However, estimating that only one-sixth of the tree becomes paper is unbelievable – so much so that I’d expect someone would have published that result and raised a hew and cry over it. So while 4,500 for a fir tree and their estimate of 1,100 seems wide apart, I’d be willing to come closer to theirs, based on wastage of (say) 50% – here then is your answer:
How much toilet paper does a tree make? A nice solid 40 foot pine or fir tree that is 18 inches wide from root to top will make about 2,500 rolls at 1/2 pound weight each. More or less.
Oh, and one more factor: Paper rolls are not all created equal. We started this journey with a measure of a roll at 1/2 pound, so feel free to tweak the math based on your estimate. But be aware that manufacturers love games with toilet paper, and toilet paper varies greatly in how much you get per roll. If you ever want to make yourself crazy, compare the actual number of sheets per roll of toilet paper in the supermarket – before the manager asks you to leave, or you start pulling your hair out, you’ll find that there is no pattern to it, and a single roll of one brand can hold more sheets than a double of another. Name brands are especially stingy with the sheets.
But regardless of the details, now you can estimate how much your favorite tree would give you in bottom-cleaning products…