I was watching Cutthroat Island this weekend with my daughter, who loves pirate movies, when I started thinking about these giant treasure chests full of gold you see in such films.
While I get that it’s a movie, it was fun to think about how practical carting around that treasure chest of doubloons might be.
- The treasure is pure, 24k gold to make the math easier rather than the 22k gold that doubloons are actually made from.
- Gold weighs 19.3g per cubic centimeter.
- The highest packing density you can get for circular objects is 90.6% but given the various ratos we could use and the notion we’re throwing coins into a chest we’re probably looking at closer to… oh, 35% packing efficiency.
- The chest weighs nothing. Or, at least, for the purposes of my little math fun here, I’m just ignoring the weight of the treasure chest proper.
Now, let’s say the treasure chest is like 90cm x 60cm x 60cm on the inside. A little large-ish, but not unheard of in a pirate movie.
- The chest has 324,000cc interior capacity.
- Multiplied by the 35% packing efficiency, you’d have 113,400cc of gold.
- 113,400cc x 19.3g per cc = 2,188,620g = 2188.62kg (4825.1lb).
There is no way pirates are carrying around 5000lb gold chests.
Let’s figure a couple guys - one on each end of the chest - need to cart the chest through the jungle or something. They’re strong, but not they’re not Hafþór Júlíus Björnsson. You’re looking at something like 115kg (253.5lb) or so lest it gets unwieldy.
Working backwards, 115kg is 5958.55cc of gold. With the packing ratio, that’s a chest with 17024.43cc total capacity. To make the math easy, let’s say it’s a cube-shaped chest. That’d yield a chest with internal dimensions of about roughly 25.73cm (10.13 inches) on a side.
That’s a pretty tiny treasure chest.
At least, tiny in comparison to what you usually see on a pirate movie.
Now, I could be generous with my packing efficiency. Maybe it’s far less than 35%, or it could be that the chest isn’t packed to the top with gold, or both.
If you had that 90cm x 60cm x 60cm chest and limited yourself to the 115kg weight, that’d put the packing efficiency of doubloons at closer to 5%; or it’d mean the chest is not quite a quarter of the way full.
Just for fun, we can also calculate the value of such treasure. The price of gold today (as I write this) is $39,175.66 USD per kg.
- 115kg of gold = $4,505,200.90 USD
- 2188.62kg of gold = $85,740,632.99 USD
If the chest was full of doubloons (which, again, are actually 22k gold, not 24k), we know that doubloons weigh 6.867g so you’d have…
- 115kg of doubloons = 16,746 doubloons
- 2188.62kg of doubloons = 318,715 doubloons
Doubloons seem to be baesd on weight rather than physical size (or, at least, I didn’t see any average size listed anywhere in my two minutes of searching) so I’m not sure how big a chest with that number of doubloons might need to be. I can’t imagine it’s too far off from my original calculation.
Anyway, it was kind of fun to think about. It makes for a better movie to have the giant chest of treasure, so it’s all good.