I wrote about what an incomprehensible number 1 trillion is. And it still IS incomprehensible to me when talking about it as a number of dollars. But there are bigger numbers, MUCH bigger numbers. For instance, there are 50-75 trillion cells in a single adult human. And there are about 20 times that many bacteria (1 quadrillion) in the same person. WOW! Or some of you might say, “YUCK!”

But the number I really wanted to discuss is Avogadro’s number which is 6.02214179 x 10²³ in scientific notation. Or written out, it is 602,214,179,000,000,000,000,000. This number is used primarily in chemistry and physics to count small particles such as atoms and molecules and is also called a mole — like 12 is called a dozen. The need for this number points out how incredibly small atoms and molecules are. There is 1 mole of molecules in:

- 18 grams (about 2/3 ounce) of water.
- 342 grams (about 12 ounces) of sucrose (table sugar).
- 22.4 liters (about 0.8 cubic ft) of a gas at standard temperature and pressure (0 degrees Celsius and 1 atmosphere).

That is a LOT of particles in a small space! However, while Avogadro’s number is usually used to quantify the incredibly small, it can be used to count anything. To help visualize how big this number is, a mole of:

- fine sand would cover the surface of the United States to a depth of 27 inches.
- unpopped popcorn kernels would cover the surface of the United States to a depth of 6 miles.
- marbles would cover the entire surface of the Earth to a depth of 1 mile.
- soft drink cans would cover the surface of the Earth to a depth of over 200 miles.
- marshmallows spread over the entire surface of the Earth would be about 20 miles high.
- pennies distributed equally to the entire population of the Earth would make each person a trillionaire. though life on Earth would be difficult being buried under 0.357 miles of pennies.
- pennies could repay the United States National Debt 434 million times.
- pennies stacked in a 6.3 meter diameter cylinder would reach 1 light year
- dollar bills in a single stack would stretch almost 7,000 light years.
- counted at the rate of 10 million per second would take 1,908,301,579 years to count.
- water drops (20 drops/ml) would fill a cylindrical column of water 6.3 miles diameter, reaching to the Moon.
- of cells is about twice the number of the cells in the entire human population of the Earth
- milliliters of water is 1/2 of the total amount of water on the Earth
- kilograms is about 1/10 the mass of the Earth.
- inches is 1,616,814 light years, or across our galaxy and back 8 times.
- seconds is about 19 quadrillion years, 4,203,307 times the age of the Earth, or 1,387,856 times the age of the universe itself.
- stars would be TWICE the estimated total number of stars in the universe

While Avogadro’s number IS a big number, other numbers which dwarf Avogadro’s number come to mind:

- the googol, which is a 1 with 100 zeros after it or 10
^{100}. When written out this is:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. - 10
^{80}or 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 which is the estimated total number of elementary particles in the observable universe. - And of course there is the largest non-finite number of all, infinity —

My goal in writing about Avogadro’s number has been to share with you my sense of wonder when thinking about these enormous numbers. I hope I have succeeded in this and would enjoy hearing your thoughts or other examples. For the truly geeky of you, the remainder of this post contains some of the constants and formulas used in deriving the examples.

Constants and formulas used in the calculations:

- Avogadro’s Number = 6.02214179 x 10²³
- surface area of the 50 United States = 9,629,091 km
^{2} - total surface area of the Earth = 5.1 x 10
^{8}km^{2} - diameter of an average size marble = 1.25 cm
- dimensions of a US penny = 19.05 mm diameter x 1.55 mm thick
- dimensions of US paper currency = 0.0043″ thick; 6.14″ long; 2.61″ wide
- United States National Debt at time of writing = $13,877,812,477,476
- dimensions of a large marshmallow = 30mm diameter; 34mm tall
- diameter of fine sand particles = 0.25mm
- diameter of an unpopped popcorn kernel = 6mm
- population of the United States at time of writing = 310,542,448
- population of the Earth at time of writing = 6,890,032,047
- volume of all the water on the Earth = 1.3 x 10
^{9}km³ - mass of the Earth = 5.98 × 10
^{24}kilograms - average surface to surface distance from the Earth to the Moon = 376,351 km
- age of the Earth = 4,540,000,000 years
- age of the universe = 13,750,000,000 years
- 1 light year = 9,460,730,472,580.8 km

highest density of circles with hexagonal packing arrangement

highest density of uniform spheres with hexagonal packing arrangement

Too deep for me ——–