Forbes math geek calculates the value of Smaug's Hobbit treasure

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Dec 14, 2012

Given that J.R.R. Tolkien's Lord of the Rings prequel is about a quest to liberate an "unassessably wealthy" dragon of his gold, silver and jewels, it does beg the question: Exactly how much is Smaug's loot worth?

According to Forbes' resident math wonk, Michael Noer—who's part of the crack team behind calculating the 15 richest fictional characters—it's relatively simple to put a current monetary value on the treasure hoard at the heart of the Lonely Mountain.

The lengths to which Noer goes to prove this, however, are anything but simple. To wit, here's how he arrives at merely the size of Smaug's treasure bed:

"The book describes Smaug as 'vast,' 'centuries-old' and of a 'red-golden color.' According to the Advanced Dungeons & Dragons' site The Hypertext d20 SRD a true-dragon of that age and color measures around 64 feet from snout to tail. However, a great deal of that length is likely tail. By way of reference, Komodo Dragons are 70% tail by length, so we can estimate Smaug's body to be approximately 19.2 feet long.

Dragons are long and narrow, so we can safely assume that Smaug can curl comfortably up on a treasure mound with same diameter as his body length—19.2 feet.

How high is the mound? Well, at one point in The Hobbit, Bilbo climbs up and over the mound, and we know that Hobbits are approximately three feet tall. Assuming the mound is twice the height of Bilbo, we can say that the mound has a height of approximately 6 feet—like a six foot tall man climbing over a 12-foot mound of coins; substantial but not insurmountable.

To keep the math relatively simple and to avoid complications like integrating the partial volume of a sphere, we can approximate Smaug's bed of gold and silver to be a cone, with a radius of 9.6 feet (1/2 the diameter) and a height of 7 feet (assuming the weight of the dragon will smush down the point of the cone by about a foot).

Now we can calculate the volume of Smaug's treasure mound:

V= 1/3 π r2 h = 1/3 * π * 9.62 * 7 = 675.6 cubic feet

But, obviously, the mound isn't solid gold and silver. We know it has 'great two-handled cups' in it—one of which Bilbo steals—and probably human remains, not to mention the air space between the coins. Let's assume that the mound is 30% air and bones. That makes the volume of the hoard that is pure gold and silver coins 472.9 cubic feet."

Whew. That right there just made my head hurt. You can bounce over to Forbes to see the rest of his calculations, but the upshot of it all is that Smaug's loot is worth $8.6 billion, give or take a magical weapon or two.

Worth questing for, methinks.

(Via Forbes and io9)