# The Pirate Treasure Chest

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.

Assumptions:

- 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.