Toothpaste Math

--Blogpost written by Bob

One of the most habitual and predictable personal hygiene we engage in is brushing our teeth.  While some of us may brush our teeth once per day and always in the morning or evening and others may do it twice a day (mornings and evenings), chances are good that we do it in the same way and at the same time(s) everyday.  For each of us, our toothpaste needs should be very predictable.  Maggie and I have different brushing habits--I am a morning-only brusher and she is a morning-and-evening brusher.

Most of us take our toothpaste for granted.  We pick it up at the grocery store
when we shop for groceries and we always have enough.  We don't 
think about how much toothpaste we use.

We both use different types of toothpaste.  I use Listerine while Maggie uses Sensodyne in the morning and Prevident in the evenings.  We can't always rely on getting our toothpaste brands in grocery stores at home, let alone in the small grocery stores along the ICW and in the Bahamas.  Since toothpaste takes up very little space, it is one of the items that we can buy online and store onboard for our entire 8 months away from our home base.

How much of each brand of toothpaste we will need for the 8 months that we will be cruising each year?

We Could Simply Guess

We could simply make a guess.  Maggie guessed three tubes of each of her two brands.  We'll see if her guess would provide enough toothpaste for the whole trip or if she will be growing moss on her teeth by the time we return.

We Could Calculate The Amount Needed

Toothpaste is measured in ounces of weight--an easy mistake would be to assume that this is fluid ounces.  A 4.2 ounce tube of toothpaste represents a volume of 3.276 cubic inches.  (The density of toothpaste is 1.3 grams/milliliter or 0.78 ounces/cubic inch.)

The net weight of the tube of toothpaste is 4.2 ounces
as shown on the above packaging label.

When we squeeze toothpaste from the tube it leaves as a cylinder roughly equal to the inside diameter of the nozzle of the toothpaste tube (measured at 0.280 inches).  The length of the cylinder of toothpaste dispensed is just short of the length of our toothbrush--approximately 1 inch.  The volume of the cylinder of toothpaste for a single brushing is 0.062 cubic inches. 

As we squeeze toothpaste from the tube it comes out as a cylinder equal 
to the inside diameter of the nozzle.  The length of the cylinder
is approximately equal to the length of the toothbrush.

Each 4.2-ounce tube of toothpaste provides 52 brushings (4.2 ounces divided by 0.062 cubic inches per brushing).  The eight months that we will be cruising is equal to 240 days.  So, we will need five (4.61 by calculation) tubes of each different type of toothpaste for an entire trip.

Summary

There are a couple other items we can calculate our needs in advance--canned cat food is one of them.  For other items we are monitoring how much we use per month and will be multiplying by eight months to calculate our needs.  We plan to buy milk, cheese, eggs, and baked goods locally as needed.

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