# Daily Tree Consumption for Toilet Paper

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

## Introduction

Figure 1: Typical Roll of Toilet Paper. (Source)

I was reading an article on National Geographic when I spotted an interesting factoid about the impact of Toilet Paper (TP) world-wide tree consumption.

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.

## Background

### General References

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).
• 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.

 Eq. 1 $\displaystyle {{m}_{{Tree}}}(d)={{e}^{{{{\beta }_{0}}+{{\beta }_{1}}\cdot \text{ln}\left( d \right)}}}$

where

• 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.

## Analysis

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.

Figure 2: Estimates of Trees Consumed By Toilet Paper Usage.

## Conclusion

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.

Figure 3: US Forest Service Formula for Tree Mass vs Diameter. (Source)

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

Save

This entry was posted in General Mathematics, General Science. Bookmark the permalink.

### 5 Responses to Daily Tree Consumption for Toilet Paper

1. Randall says:

I think I'm probably being stupid here, but, I'm going to ask the question so that someone can tell me what's wrong with my understanding. It's just to do with the opening paragraph: surely "international Internet traffic" between say France & Germany or Canada & the USA is not carried by submarine cable?

• mathscinotes says:

You are correct. I should have said "Transoceanic". I will correct.

mark

2. matt says:

Does this mean virtually nothing is transmitted via satellites?

• mathscinotes says:

It is an order of magnitude thing. Satellites handle megabits per second. Fiber can handle terabits per second. See this post. For typical examples, see here. For an example of a high-speed satellite data link, see this page on TDRS.

mark