Quote of the Day
When the satisfaction or the security of another person becomes as significant to one as one's own satisfaction or security, then the state of love exists. Under no other circumstances is a state of love present, regardless of the popular usage of the term.
— Harry Stack Sullivan
Toilet paper wipes out 27,000 trees a day.
Like many factoids, I doubt there is a way to actually measure this number – it can only be estimated. Thus, it is a prime candidate for a Fermi solution.
I see factoids like this all the time. My favorite factoid in the fiber optic business is that 99% of the transoceanic Internet traffic is carried by submarine cables. If you ask around, no one can tell you how the remaining 1% is carried – 1% of total transoceanic bandwidth is a lot of bandwidth for non-fiber transports (e.g. Iridium, TDRS). I heard a submarine cable expert say that 99.999% is probably closer to the true value, but people hedge their numbers by saying 99%. A better answer is that virtually 100% of transoceanic Internet traffic is carried by submarine cables, and the tiny amount not carried by submarine cables is so small that no one knows what it is. An example of a place requiring transoceanic data service and that has no transoceanic fiber access is Antarctica.
The following links provided me some good background for the analysis that follows.
- National Geographic article mentioning the factoid (Link).
- Blog post on toilet paper rolls per tree (Link).
- Typical toilet paper measurements (Link).
- Tree pulp statistics (Link).
- Wikipedia on tree pulp (Link).
- General toilet paper info (Link).
Some Tree Statistics
The journal Nature reports that:
- The world is home to more than 3 trillion trees.
- People cut down 15 billion per year.
- The number of trees has declined by 46% since the beginning of human civilization.
Average Mass of Harvested Tree
The mass of the average tree harvested for pulp can be estimated using Equation 1, which is an empirical formula developed by the US Forest Service. This formula gives us the typical mass of a tree based on it diameter. The parameters are species-dependent. For this exercise, I assumed the trees are aspens, which are commonly used for pulp where I live. The specific parameters (β0, β1) are given in Appendix A.
- mTree is the mass of the tree [kg].
- d is the diameter of the tree measured at breast height [cm]. This parameter is often referred to as "d.b.h."
The US Forest Service has a number of other mathematical models for tree mass versus diameter. I chose this one because it was easy to code.
Figure 2 shows my analysis. I included many comments in-line, so I will not go through the details in my introductory text. For those who want to view my source, I include it here.
I can see where the 27K number is plausible. The actual number of trees cut for use in toilet paper is probably unknowable and can only be estimated. Unfortunately, the analysis is sensitive to parameters that are highly variable:
- percentage of people that use TP.
- amount of TP used per person.
- diameter of trees harvested for TP.
I suspect that the 27K trees per day number is probably low. Even with the uncertainty involved, it is an interesting number because it shows the environmental impact of a small item can be substantial if enough people use it.
Appendix A: Formula for Tree Mass vs Diameter.
Figure 3 shows the formula that I used to estimate the mass of a tree based on its diameter.