Science-abuse

Science in movies and video-games

How much is Smaug's gold from the Hobbit worth ?

01/08/2018 ⋅ 8 comments

Par Timo van Neerden

The Hobbit is a film series based upon the novel The Hobbit by J. R. R. Tolkien.
The story is about a hobbit, Bilbo Baggins, during his journey, accompanied by Dwarfs, Elves, Wizards and many other creatures from the Tolkien universe.

In the story, a group of dwarfs wants to reclaim the gold of their ancestors. That gold is stored in a fortified mountain, which caves are filled with an immense treasure that once has been stolen from them by a giant fire-spitting and very miser dragon: Smaug.

de l’or partout
It is in the second and the third movie that we encounter the treasure… and the dragon.

My purpose here, in this article, is to estimate the amount worth of gold that we see in the movie (I’m not considering the books).

Methodology

œil de smaug
Several scenes in the movie grant us an overview of the gold stored in the mountains. We also see the dragon, and with him, its size and the place he takes in the cave.

We also see a room with a “swimming pool” full of molten gold, in which Smaug drowns and Thorin (one of the dwarfs) progresses. The volume of the pool is quite easy to estimate: it’s just a parallelepiped, which size can be found by using Thorins height and Smaugs sizes. The other parts of the treasure will be far more difficult to estimate, but I’ll do my best anyway.

I’ll start by found out the size of the dragon, then measuring the swimming-pool of gold. That will give us a start point for the totality of the gold.

With successive estimations of the coins, the dragon, the cave, I’ll manage to find out how much gold is in there, and then I’ll estimate its net worth based on the current gold prices.

Let’s consider that all the coins have all the same dimensions of 5 cm (~2 inches) in diameter.

Smaug's length

smaug
With gold coins as a reference (5cm / 2 inch) and several pictures from the movies, I deduce that it’s eye measures about 25,9 cm (10 inches), that the distance between his eyes is 3,02 meters (9.9 feet), and his face is 5.23 metes across (17.3 feet).

Using that, its body is about trice that size in height. If Smaug was asleep, curled on himself like a sleeping cat, the highest point of its back would be about 15 meters (49 feet) above the floor.

This seems huge, but come on: it’s a dragon!
Besides, when he destroys the village on the lake, he out-sizes all the buildings, and his wingspan is a good fraction of the whole city. Take this into account and 15 meters (49 feet) seams quite reasonable.

Amount of gold in the “swimming-pool”

In the movie, the dragon totally disappears in the gold. This means that the pool is at least 15 meters (49 feet) deep. Besides, considering the width of Thorin — 1 meter (3 feet) — relative to the pillars, the pool measures roughly 130 meters (426 feet) long and 55 meters wide (180 feet).

thorin sur le bassin d’or
The total volume of gold in that pool is then 130×55×15 = 107'250 m³ (about 3,78 million cubic feet) . The whole weighing 2'069'925 metric tons!
If all this gold was a perfect cube, it would be 47 meters (154 feet) in side. About the same size as two Arc de Triomphe monument, from Paris, side to side.

This is already tremendous amount of gold. The price of all this would be about 83 trillion USD (having the price of gold, that is about ~40 000 USD per kilo). It’s about the worlds GPD in 2012. And we have only started…

In the real world, all the gold humanity ever extracted since like, forever, would fit “only” in a cube of 20 meters (65 feet) of side. In that pool alone, we already have more than 13 times the worlds amount of gold.

The other gold pieces

The remaining gold is everything that sits in the caves, mainly in the form of coins.

It’s quite difficult to estimate all this: these mountains of gold are not uniform and, more importantly, there is empty space between the gold coins.

For the mountains of gold, I can estimate a mean size. Smaug, the dragon, sleeps totally under the coins. The hills of gold are at least 15 meters (49 feets) height. At some other places, the floor is visible: there is no gold (0 meters).
The hills and the dales are about uniformly spread in the cave, so let’s say that the mean height of the coin layer is about 7.5 meters (25 feet).

For the other dimensions, we can use, again, the previous dimensions of the dragon:

smaug et l’or
We now know that Smaug measures roughly 60 meters (200 feet). This is also in accordance with several other estimations (here or here).

There is room enough in that cave for about ten Smaugs, in all the directions, according to the different scenes in the movie. We can assume that the cave measures about 500 meters (547 yards) wide and long. Yes, that’s a lot of space! …and a lot of gold too!

The volume of gold coins is thus: 7.5 × 500 × 500 = 1'875'000 m³[/b] (66 million cubic feet).

But this volume is that of gold coins, not a solid lump of metal. We have to find out how much gold that is and how much air there is in between.

To do that, I did the experiment myself: I have a bunch of coins here (not of gold, unfortunately :D). I put the coins in a drinking glass (150 cm³) and filled the space between the coins with water. Then, I drop the coins out and measured how much water remained.

As result, I got:

  • 80 cm³ of water
  • thus 70 cm³ of coins.

The coins count thus for 46 % of the space.

That for, in those 1'875'000 m³ (66 million cubic feet) of coins, there is room for 862'500 m³ (30 million cubic feet) of solid gold. This is as much as 9 Olympic pools filled with solid gold. It would weight 16'646'250 metric tons, and would be worth 676 trillion USD.

Smaug's wealth

les nains et l’or
I don’t know if we can still talk about “wealth” here : if only Smaug was real, it would be 12'000 times richer that Bill Gates.

This is ridiculous… He would own 11 times the entire worlds GPD, and would be equivalent to about 70 times the total amount of bank notes and bank coins available in the entire worlds (this amount is called M0), and more than 5 times the total amount of money (coins, notes, bank accounts, virtual money…) on this planet (this is called M3).

Smaug is 5 times richer than the entire humanity. Only in gold.

We can however mitigate this a little bit.

In real life, gold prices go up and down according to demand and supply. If suddenly a huge amount of gold would be added to what we have, gold would be less scarce and its price would go down. Accordingly to previous estimations, Smaug has got a little more than 100 times the world amount of gold. I’m no expert, but considering that, we can divide that price of gold by a factor of 100 as well, and this also goes for his wealth.

On the other hand, all that new gold would also generate a new demand and gold prices would go up again.
As of today, all our gold tools are tiny because gold is precious and rare. If gold suddenly becomes abundant, we could make everything we wanted out of it and it would no longer be as expensive and rare. Let’s say, a bit haphazardly, that the prices would go down a hundred times first and then go up four times, as new demands kicks in.

As a result, gold prices would go down only by a factor of 25. In other words, it would only be worth 4% of it’s actual price. Smaug, who possesses 99 % of all the gold in the world would then only have 300 times Bill Gates Wealth, thus only about 13 trillion USD. Poor little thing…

And according to Forbes?

smaug and the giant statue of gold
For years now, Forbes magazine famously ranks the worlds wealthiest people in the world. They also set up the same ranking (for humoristic purposes) for fictional creatures. We find Scrooge McDuck, Tony Stark (Iron Man), Bruce Wayne (Batman)… aaand Smaug!

In 2013, Smaug was ranked second richest fictional creature, right behind Scrooge McDuck, but ahead of Tony Stark and Bruce Wayne, with 54.1 billion USD.

This is still a huge amount of money, but it’s far from my 13'000 billion USD. The difference come from, I guess, that they used the amount of gold as described in the books, not in the film, as I did.

I don’t think that I did any miscalculations here. I did however many approximations, but in each cases, even if I had exaggerated 10 times, or even 100 times (which is a very, very large error), Smaug would still be twice are rich as Bill Gates, and that, today, is something only a real dragon, like Smaug, could say.

8 comments

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Lucas13/12/2019 à 06:16:03

“Grant,” not “grand.” Learn to write. Maybe then we could take your math seriously.

@répondre #lien

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Percy Jackson13/12/2019 à 15:31:38

"you cant spell so you must be bad at numbers"

#Einstein

@répondre #lien

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John Dil Doe13/12/2019 à 18:30:02

Smaug is dead. All the gold & gems & mithril inherited Durin's sons.

@répondre #lien

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timo14/12/2019 à 18:08:15

@Lucas : One mistake in 1800 words in a language I’m still learning. Now it’s gone ! Thanks !

@répondre #lien

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Pete14/09/2020 à 18:48:53

hey timo, nice estimating, but I think you are a little off in some numbers. when smaug wakes and bilbo first goes invisible, smaug's eye is roughly the same size as bilbo or about 1 meter. if you notice, the eyes are side mounted, not forward, so they may be under a foot looking from the front, but not from the side. the face seems a tad narrower than your 5 meter estimate, perhaps more like 3-4 meters. the length is seriously under estimated though. the head length is about twice the width, or about 6-8 meters. the neck is about 4 times the length of the head, or about 24-32 meters, making the head and neck 30-40 meters. the torso length is about equal to the head and neck, or another 30-40 meters. the tail seems to vary from 3-5 times the torso length in different movie scenes, or 90-200 meters. that gives a total length of 150-280 meters. the wing span appears to be roughly equal to the length. perspective seems skewed in different scenes, so it is hard to define exactly. compared to the size of the treasure hoard room, scenes that show bilbo walking through it seem to show the pillars to be about 20-30 meters apart, with smaugs head in front of one pillar and his neck and body wrapped around the first pillar and another behind it, with the tail wrapping around and to the side, which implies a good 4-5 times the length between the pillars, or about 80-150 meters. assuming a good portion of the tail was buried and didn't show up in the treasure hoard scene, that raises the length a bit, but still well below the high end of the 150-280 meter range, so the length is more likely at the low end of the 150-280 meter range, or about 150 meters. the height of the back of smaug at rest does seem to be about 10-15 meters though.
the treasure hoard room looks to hold about five pillars long and wide, or about six times the pillar to pillar gap, making the room 120-180 meters in each direction, which is much smaller than the 500 meter by 500 meter size you assumed. since the whole room is never fully shown, it is difficult to argue between your size estimate and mine, but underground caverns 500 meters wide would seem to be a tad rare. the gold pile in the room slopes upward to the walls behind smaug, but downward from smaug to the stairs until the floor is almost bare. that gives an average height of the pile about equal to smaug's sleeping height at his back. call it about 10 meters thick across the whole room. that gives a total volume of 144-324 thousand cubic meters. you are right about the space between coins, that is called void volume, and the fraction of void volume is called void fraction. dry solids vary quite widely in void fraction, from nearly zero for closely packed cubes to as much as 80-90% for highly irregularly shaped chunks, so your estimate from your coin example is reasonable, so I assume 50%. that gives 72-162 thousand cubic meters of solid gold. at 19.3 tonnes per cubic meter, that works out to 1.4-3.1 million tonnes (tonne = metric ton = 1000 kg). the trouble is that all the gold that has ever been mined only adds up to about 190 thousand tonnes. so just smaug's treasure hoard that he was sleeping in is something like 10 times all the gold that has ever been mined on the entire earth. that doesn't count the gold in the furnaces that gets poured into the king statue before it collapses into the "pool". sadly there are massive discrepancies there too.
the movie showed only four furnaces, which just happened to have melting pools filled with gold coins for some reason, and they looked to be 10 meters across and maybe 5 meters deep. the melting pools were hexagonal, but I approximated it as circular, so the volume holds roughly 393 cubic meters. all four furnaces thus hold about 1571 cubic meters. the trouble there is the melting pools held coins, which should have the same 50% void fraction to give 785 cubic meters of actual gold. meanwhile the king's statue stands about the same height as the hall of kings is wide, roughly 50 meters. the width of the statue looks to be roughly 15 meters wide and about 8 meters thick. that works out to 6000 cubic meters if assume those dimensions are average. so the question becomes, how do four furnaces totaling only 785 cubic meters of gold manage to fill an entire statue that should hold closer to 6000 cubic meters? it can't have already had a bunch of gold in the statue either, because the entire statue collapses, meaning the whole contents had to be semi-molten.
oddly enough, the hall of kings looks to me to be about 50 meters wide (you estimated 55) and 100 meters long (your estimate was 130), but the really odd thing about that hall is the depth of gold only seems to be about 1 meter deep. so how is the dragon submerged? the size works out to 100x50x1 = 5000 cubic meters, which is roughly equal to the 6000 cubic meter statue estimate, so maybe the depth was a tad over 1 meter (1.2?). for the dragon to be submerged entirely, the "pool" would have had to be at least 15 meters deep, but the dragon gets up after being dunked and walks out of the hall without its feet splashing, as if the "pool" was only inches deep. so the amount of gold in the "pool" changes by a factor of 10 higher for the dunking and a factor of ten lower for the exit from the hall. if the statue is right, the pool was only about 1.2 meters deep, and there would have had to be closer to 32 furnaces with the same size melting pools, not just 4. that would make the 6000 cubic meters volume consistent though. that amount is dwarfed (pun not intended) by the treasure hoard though. it would make the total 78-168 thousand cubic meters of gold, or 1.5-3.2 million tonnes.
here is where it gets REALLY fun though. how much is that worth? well there is 32.15 troy ounces per kilogram, and current gold price is roughly $1800/troy ounce, so 1 tonne is worth almost $58 million, which makes the total worth roughly $87-185 TRILLION in current dollars, which is indeed still greater than the entire net worth of the global economy. perhaps gold was much cheaper in the past, but the economy was substantially smaller too, so that is probably a wash.

@répondre #lien

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Taelessan Mordalan Wavedancer19/09/2020 à 21:34:16

Missing fact that the treasure hoard not just coins, but goblets, cups, cutlery, candelabra, weapons, rings, necklaces, bracelets, torcs, precious stones etc ...eg all of the Dwarven Goldsmith/ Weaponsmith/ Armour Smith forged artefacts crafted. Also a large portion of the Treasure Hoard not just Dwarves wealth from Erebor but from Smaug's other sackings, presumably Smaug gathered some hoard in Grey Mountains before migrating south to escape attack by other would-be hoard stealer dragons. He also sacked Esgaroth & Dale & would have carried off hoard from that human kingdom as well. Possibly he even raided further west, south & east too.

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timo04/11/2020 à 09:28:03

@Pete :
@Taelessan Mordalan Wavedancer :

Thanks for your enlighting comments.

Indeed, this is all a rough “guestimate”, and only based on the gold itself, not the added vallue of the goblets, coins or other art forms made out of the gold.

Also, the scales used may vary more or less depending on the images of the dragon, or Bilbo himself.

Therefore, the only conclusion one should realy consider is “Smaug is very very very wealthy” or “there is more wealth inside that mountain than in our entire world”.

@répondre #lien