When the fellowship journeys through the long dark of Moria they at one point arrive at one of the Great Halls of Khazaddûm. This is where Gimli sings to the fellowship of Durin and the Dwarrowdelf (changed to Gandalf briefly mentioning it in Peter Jackson’s adaptation).
The Dwarrowdelf in Peter Jackson’s LoTR
“There must have been a mighty crowd of dwarves here at one time ‘ said Sam; ‘and every one of them busier than badgers for five hundred years to make all this, and most in hard rock too! What did they do it all for? They didn’t live in these darksome holes surely? ‘ ‘These are not holes,’ said Gimli. ‘This is the great realm and city of the Dwarrowdelf. And of old it was not darksome, but full of light and splendour, as is still remembered in our songs.” [LoTR  FoTR  Journey in the Dark]
At which point our friend Gimli begins to chant of the city of old.
Reading this passage again recently, a tiny question popped into my mind… “could Khazaddûm really have been built?”. A question that didn’t go away either and starting gnawing at me until I finally did it justice by doing a bit of research and crunching some numbers. Obviously we have (unfortunately, as usual) little factual numbers to work with from Tolkien’s writing, so we must base ourselves on what little we do know and what conjecture could be valuable for this exercise.
So, what exactly do we want to find out here…
Could Khazaddûm actually have been built beneath the mountains?
To answer this question we have a multitute of variables to take into account, being amongst others: the density and weight of the Mountains, the amount of dwarven workers, dwarven excavating techniques, workhours per worker, strenght of each worker, system of rubble removal, etc… .
So let’s start with our facts and data we can deduct from these fact.
Khazaddûm was delved under three mountains; Bundushathûr (Cloudyhead), Barazinbar (Redhorn) and Zirakzigil (Silvertine). Unfortunately we do not know the actual height or base diameter of these mountains. We could however base ourselves on maps to find out the base diameter of these mountains. With a perfect conical mountain, the base diameter is usually twice the length of the actual height. So, this means that if we found out the base lenght of these mountains by studying Tolkien’s map in more detail we would be able to deduct the estimated height.
Conical Shape
With both height and base we could make a decent estimate at the weight of this range.
Though we are able to find maps that feature the Misty Mountains, of which these three peaks are part of, it’s a bit of a challenge to find an original map that features these three mountains prominently.
Hence me basing myself on a map featured on The Encyclopedia of Arda. Based on this map our mountains would end up with the following specifics:
Thanks to The Encyclopedia of Arda http://www.glyphweb.com/arda/
Mountains of Khazaddûm
Bundushathûr Height 
3500

Bundushathûr Base 
7500

Bundushathûr Cubic M 
206,167,017,892

weight in tons 
992,188,732,273

Barazinbar Height 
4500

Barazinbar Base 
9500

Barazinbar Cubic M 
425,293,105,480

weight in tons 
2,046,743,613,431

Zirakzigil Height 
5000

Zirakzigil Base 
12000

Zirakzigil Cubic M 
753,982,236,862

weight in tons 
3,628,575,935,169

Connecting Passage Weight (tons): 
1,000,126,242,131

KhD Mountains weight (tons): 
6,667,508,280,874

Total KhD Range weight (tons): 
7,667,634,523,005

So, what do the above numbers tell us really?
In short, the range of the three mountains above Khazaddûm (mountains and connecting passages and plains) would weigh 7.6 trillion tons. With the ice and snow on top of these it would likely be closer to 8 trillion tons.
For those that wonder, I calculated the weight based on the average weight per cubic centimeter of earth (5.5gr) and granite (2.8gr), using a 75/25 ratio (a bit more then usual in most mountains – taking into account Sam’s comment “and most in hard rock too! ” ) Metals such as gold, silver or even mithril in this case would not even account for one thousand of a percent of the total weight of the mountains. Yet to be as complete as I can be, I’ve taken all this into account, and came up with an average weight per cubic centimeter of 4.813 gram.
Now you might wonder what the weight of these mountains has to do with the whole question we’ve asked.. well we’ll come to that a bit later.
Let us focus first on the key question here.. How many Dwarves would we have needed to excavate Khazaddûm to the size we know from the books? Without question Khazaddûm was beyond vast. By the time of the Balrog (T.A 1980) thousands of smaller and larger mansions would have been build/excavated to house the growing number of Dwarves. Bring into that equation the Great Halls and the Smaller Halls and the numerous passage ways, this mammoth construction task would make the Great Pyramid of Giza look like a tiny LEGOset. So, how many Dwarves would we have needed to actually have completed this “job” ? And would there have been enough of them around to build Khazaddûm in the first place ?
In order to come up with an answer to this question I based myself on the Khazaddûm we find in Turbine’s LoTRO.
Is this the definite answer to the inner size of Khazaddûm ? No, it isn’t… that I fear rests forever in the genius mind of Tolkien himself. But to be frank, Turbine did a brilliant job at capturing the vastness of the Dwarrowdelf and in my view comes close to the vastness described by Tolkien. So let’s crunch some number shall we…
Sizing up and adding up all the Great Halls, Small Halls, mansions, passage ways and mines we find in our virtual LoTRO Moria a grand total of no less then 1.5 billion tons of excavated matter. To give you an idea this rubble pile could have made a small mountain/large hill on its own with a height of about 500 meters.
We know that the vast majority of the Khazaddûm would have been completed by the mid of the Second Age (when the friendship with the Elves of Eregion was at its height and the WestGate would have been built). Seeing that Durin the Deathless would have founded his seat of power back in the year of trees, we are looking at roughly 6000 years of construction time.
Moria West Gate
Now add to that the concept that Dwarves are very hardy beings, that live more then twice as long as men and are expert delvers, we start to get a good idea of how many delvers we would have needed to complete this epic monument that is the Dwarrowdelf.
Let’s say our average dwarf works for 150 years (excluding their youth and old age), hardy as he is he can work 12 hours a day (forget the MiddleEarth union for minute).. and would work about 300 days a year (apart from the Dwarven holidays these lads would be delving away). Being stronger than men we can safely say these dwarves would have had no problem with cutting away 30 kilos per hour (which would be twice as much as what men would have been able to on a very good day, in present day). So with all these founded assumptions… we can work out that we would have needed a workforce of 2381 dwarves (on average) each generation. Each dwarf excavating about 16 tons of rock over their lifetime. If the above were true, Khazaddûm could indeed have been completely built by mid Second Age.
These figures aren’t pulled out of thin air either as Gimli gave us a very decent hint at the construction fury of the dwarves:
At the Hornburg: “Ever my heart rises as we draw near the mountains. There is good rock here. This country has tough bones. I felt them in my feet as we came up from the dike. Give me a year and a hundred of my kin and I would make this a place that armies would break upon like water. …Sleep! I feel the need of it. Yet my axe is restless in my hand. Give me a row of orcnecks and room to swing and all weariness will fall from me!” [LoTR  The Two Towers  7 Helm's Deep]
This may have been a bit of boasting on Gimli’s part, though I doubt it myself. Still, Gimli seems quite convinced that a hundred longbeards could construct a massive defensive structure in only a year. Which strengthens my earlier suggested numbers on dwarven work ethic.
The big question now is, would there have been at least 2381 dwarves ready for delving each generation ?
Dwarf miner by Vikingair Thane
Short answer… eventually YES. The first generations, at the time Durin the Deathless founded Khazaddûm, would have been too few to complete anything more than a few mansions and perhaps a small hall. But after about 30 generations the numbers would have been enough for the dwarves to go into overdrive and create massive construction works, such as the endless stair, many of the great halls and eventually passages to the West leading to the Hollin Gate. So work on Khazaddûm would have started very slow, due to the very slim number of dwarves around. At the end of the first age, when many of the Firebeards and Broadbeams fled to Khazaddûm (after the Halls of Tumunzahar and Gabilgathol fell to ruin), there would have been more than enough dwarves around to reach our minimum number of 2381 dwarven workers.
It would be fair to assume that the workers that actually delved the Dwarrowdelf would likely not have been the largest group of workers by the start of the Third Age. As by this time most of the grand constructions of Khazaddûm would have been completed and mining for Mithril would have become the highest priority.
Which leads me to a little bonus point in this article.
Bilbo/Frodo’s Mithril Courslet
How much mithril would the dwarves have mined by T.A 1980?
I know, I know, this is based on a zillion variables and would be as accurate as pinning answers on a board and throwing a few darts at them. Still, that won’t stop me to have a bit of fun and come up with a somewhat educated guess.
“‘The wealth of Moria was not in gold and jewels, the toys of the Dwarves; nor in iron, their servant. Such things they found here, it is true, especially iron; but they did not need to delve for them: all things that they desired they could obtain in traffic. For here alone in the world was found Moriasilver, or truesilver as some have called it: mithril is the Elvish name. …… ‘Mithril! All folk desired it. It could be beaten like copper, and polished like glass; and the Dwarves could make of it a metal, light and yet harder than tempered steel. Its beauty was like to that of common silver, but the beauty of mithril did not tarnish or grow dim.” [LoTR  FoTR  Journey in the Dark]
What does the above tell us… Mithril was a very light metal and the mining industry of Khazaddûm was aimed at it exclusively. We also know the dwarves were relentless at finding new veins of Mithril, eventually leading to their own doom. So, without much shame, here come my darts…
1) Mithril was nearly as light as water (1.05 grams per cubic centimeter)
2) It was common at first in Khazaddûm (likely slightly less common as gold would be, yet at lot less frequent than iron ore), but became ever more rare as time went on.
3) We know these mountains contained gold and jewels, so taking real life examples of mountains that also contain gold and jewels, we can estimate how much of these metals would have been in these mountains.
As a result: The three mountains of Khazaddûm likely contained over 100 tons of Mithril. That sounds like a tremendous amount at first, yet is not even one billionth of the total weight of these mountains, making it extremely hard to find. And once the first larger veins were excavated the price of mithril would have gone “beyond price”, forcing the dwarves to delve deeper and deeper for it, as we know. By T.A 1980, some 9000 years since the founding of Khazaddûm, it is extremely unlikely the dwarves would have been able to find more then 1% of that total mithril weight.
Giving us a bit more than 600 kilos of truesilver. If you think that thousands and thousands of dwarves would have been delving for generations to gather this “small” amount, you quickly think at how rare a mithril shard would have actually been. The average dwarven delver would likely not even have found a handful of it, over his entire lifetime.