I have heard the phrase several times lately. “Flat as a pancake.” I started wondering just how big a really flat pancake would be.

Most of the pancakes I’ve seen lately seem to be about 6 inches in diameter and about ¾ inches think.

Here’s a view of the pancake with measurements.

I am going to make several assumptions about pancakes.

1) I will assume all the molecules that make up a pancake are sucrose-like molecules.

2) A flat pancake is one sucrose-like molecule in height.

Let’s start by determining the number of sucrose-like molecules in a pancake. To do so, we need to know the radius of such a molecule. As best I can find, the effective radius of a sucrose molecule is 0.44 nanometers (nm).

I am pretty sure that pancake molecules are made of more than just sucrose molecules so I will assume that a pancake molecule is bigger than a sucrose molecule. I will assume a pancake molecule has a radius of 1 nm.

The measurements of the pancake in the first graphic are given in inches. The measurement of the pancake molecule is given in nanometers. Lets convert all measurements to nanometers first then to inches. This seems reasonable to me since I have never ordered pancakes in the metric system.

Here are the conversions factors we need.

1 meter = 1,000,000,000 nanometers. 1 m = 1,000,000,000 nm
That’s right. There are 1 billion nanometers in a meter.

1 meter = 100 centimeters. 1 m = 100 cm

1 inch = 2.51 centimeters. 1 in = 2.51 cm

Geometrically, a pancake is essentially a cylinder. The volume of a cylinder is the area of its base times its height. That is,

Using our measurements,

Now, let’s get these nanometers converted to inches.

We’re getting closer.

There are 1,000,000,000 nanometers in 1 meter. A centimeter is 1/100 of a meter. So,

But since there are 2.51 cm in 1 in, there are 2.51 x 10,000,000 nm in 1 in.

Cube each side to get the number of cubic nanometers in 1 cubic inch.

This number is so big, my calculator went to scientific notation to describe it. To get the number into standard form, move the decimal point 22 places to the right. Its HUGE! We’ll leave the number in scientific notation for convenience.

Our pancake has a volume of 21.2 cubic inches. That corresponds to a volume of 3.35 x 10^23 cubic nanometers.

So, a 6 inch diameter, ¾ inch high pancake has a volume of about 3.35 x 10^23 cubic nanometers.

Now we are assuming that our pancake molecule has a radius of 1 nm. If we assume the pancake molecule is somewhat spherical, it has a volume of about 4.2 cubic nanometers.

Now we’re close.

The volume of the pancake is about 3.35 x 10^23 nm^3.

The volume of a pancake molecule is about 4.2 nm^3.

There are about (3.35 x 10^23)/4.2 = 8 x 10^22 pancake molecules in a pancake.

If we were to place these pancake molecules in a line, that line would be 1.6 x 10^23 nanometers long.

Let’s convert to inches. Recall that we had computed that there are 25,100,000 nm in 1 inch. This gives us a length of 6.4 x 10^15 inches.

This length is probably out of our experience. Let’s convert to feet. Dividing 6.4 x 10^15 inches by 12 inches gives us about 5.3 x 10^14 feet.

The molecule line is about 530,000,000,000,000 feet long.

Hmmm. Let’s convert to miles. Dividing by 5280 feet gives us about 1.01 x 10^11 miles.

The molecule line is about 101,010,101,010 miles long.

The distance from the Earth to moon is about 238,857 miles.

Our pancake molecule line would extend to the moon and back about 423,000 times.

Saturn is about 8,933,750,000 miles from the Earth.

Our pancake molecule line would extend to Saturn and back about 11 times.

The Sun is about 93,000,000 miles from the Earth.

Our pancake molecule line would extend to the Sun and back about 1086 times.

Surely you agree that this is one LONG pancake molecule line.

There is something to say about packaging.