Finally, Answers For Every Question You Had About Pencils!

Inq's Pencils - Fall 2020 Curiosity Box

If you search the internet, you’ll find an (unsupported) common urban legend that the average pencil can write a line 35 miles long and write 45,000 words. That would mean each word has 50 inches of writing in it – over four feet. Maybe the person in this legend likes really big letters. 

 

So what’s the real figure?  There aren’t many data points on this, but we do have some clues :

  • A few people have made detailed calculations of how much or far a pencil can write, based on the volume of the pencil lead compared to the amount of graphite in a pencil line
  • Several have tried to find out through experimental conditions: writing out as many words as possible with different pencils
  • Others have made a machine that draws a pencil lead in a continuous, miles-long line (that last one is courtesy of our friends at Mythbusters, Jr.).

 

Analyzing these findings, it seems that the average, standard pencil can write about 80,000 words, or draw a line that’s about 3.5 miles long – depending on hardness of the lead, writing pressure, and other factors, of course. That’s not bad; at a fairly reasonable 200 words per page, you’ll get 400 pages out of a single pencil.  And we’re giving you ten: 4,000 pages worth!  When you win the Nobel Prize in Literature, please remember us.

 

Like coal and diamonds, the “lead” of a pencil is made almost entirely of carbon atoms (along with impurities like clay as binding agents), in a form known as graphite. Which means it’s also possible to calculate the number of carbon atoms in your pencil lead, using the volume of pencil graphite (roughly 2.1362830044411 centimeters3), the mass of graphite (4.83 grams, at a density of 2.26 grams/c3), the molar mass of carbon (12.011 g/mol), and Avogadro’s number (6.022 x 1023).  Put all that together, and we find that there are 2.4216918 x 1023 atoms of carbon in a standard pencil lead.  Since the average pencil is 17 cm long, that means there are 1.4245246 x 1022 atoms in every centimeter of the pencil, which you can keep in mind as you sharpen your ruler pencils and – if you’ve got really, really small handwriting - you can write that along the side: 14,245,246,000,000,000,000,000 atoms per cm. 

 

If you took the all those carbon atoms in the lead turned them into a diamond, how big would it be? Because diamonds are formed under enormous heat and pressure, there’s a common misconception that a lot of carbon gets crushed down to make a smaller diamond – like when you see Superman take a big piece of coal and squish it into a tiny diamond.  But a diamond isn’t a superdense hunk of coal or graphite; the difference between a hard diamond and a soft piece of graphite pencil lead isn’t primarily one of density, but of structure.

 

A diamond is very hard because of the lattice structure in which the atoms are arranged; the extreme pressure is what causes the atoms to align in this configuration). The carbon atoms in the graphite pencil lead are arranged in sheets, which can slide across one another, making the graphite feel soft.  In fact, if you want to go the other way, it’s possible to turn diamonds into graphite by heating them in an oxygen-free environment or blasting them with an x-ray laser. 

 

So back to your pencil diamond! Diamonds are a little bit denser than pencil graphite, so it will be a little bit smaller than what you start with: you’ll get a diamond about 65% of the size of the graphite pencil lead and weighing a little over 24 carats! Which is pretty amazing, though if you’re about to propose to someone, we don’t recommend just holding out a pencil to your beloved. Though you may be able to impress them with your newfound appreciation of the incredible, humble, pencil…