tolkiens legendarium - How large was Khazad-dûm?

Khazad-dûm is said the be the largest of the Dwarven kingdoms. In terms of scale how large was it? 40 miles end to end but how many levels?

Is there a way to compare it to a modern day city in terms of total size and population at its peak?

Answer

Being described as a vast Kingdom, Moria's greatness was unimaginable to many dwarves, even those of other mountain kindreds.

“The Mines of Moria were vast and intricate beyond the imagination of Gimli, Glóin’s son, dwarf of the mountain-race though he was.”
_{The Fellowship of the Ring: Book Two - Chapter 4, A Journey in the Dark}

The fellowship find themselves under Celebdil, however as Gandalf says, the real prize of Moria is found in the deeps under Caradhras

“The lodes lead away north towards Caradhras, and down to darkness. The Dwarves tell no tale; but even as mithril was the foundation of their wealth, so also it was their destruction: they delved too greedily and too deep”
_ibid.

Reminding us that the Dwarves had indeed dug deep. Deep enough to awaken a very old evil that was trying to hide until its Master returned.

The two parts

It's generally accepted that the Moria was built in two parts. The city towards the East, near the bridge and the 7 levels. This is where the great halls were and it's structure was likely very different to the rest of Moria. Having been built in 7 levels and 7 deeps. The image below gives us an idea of the height of the 7 levels and the location of the first deep. Considering the 7 levels cover about a mile of space, each level is likely around 700 feet high, leaving around ~50 feet between levels. Although most halls were likely much smaller than this height, one can imagine the immense size of the halls.

The depths of the deeps is unknown, but they didn't stretch past the abyss. They were likely of similar size to the levels and one could predict it to be around a mile deep.

Just how deep?

The depth of the mines has been addressed in this answer here, and although it doesn't come up with much evidence, it gives a pretty good picture of just how deep it may go.

How long was it then? How wide?

Now we have the length, as you say it's about 40 miles from East to West, however we have not established its width. We know that it is situated under the three peaks; Caradhras, Celebdil and Fanuidhol. This means it must be reasonably wide. Just how wide is not canonically known, statistically, but is slightly more obvious in Karen Wynn Fonstad's Atlas for Middle-earth.

From her map she suggests it's around 40 miles from Celebdil to Caradhras and another 20 from Caradhras to Fanuidhol. This seems to agree with the the time it took for them to travel from the Redhorn Pass to the Gate, and seems reasonable for Mountain ranges. Now if we look at the next image from Karen's maps, we can get a measure of the height of the Mines.

Please note this map has a vertical exaggeration of 7:1. This means that its real horizontal:vertical ratio is 7 times larger. This means the vertical height according to this is about 3 miles to the Guardroom. However the guardroom had a well go down from which drums were heard. Let's say we approximate it to be around 4 miles high in total, from Durin's Tower down to the bottom of the well.

So we've got this shape that's about 40 miles wide, ~40 miles long, and has a little bit sticking out (Fanuidhol), like an L-shape. It's around 3 miles high at Celebdil, with Caradhras and Fanuidhol likely a little smaller.

Comparison to the Real World

With that size, lets look at real world cities that are big. If we assume a triangle, we get a area of around 450 square miles, which equates to 1170 sq km. From here we see this is about the same size as Cincinnati, Montreal and Sydney, and around 13 times the size of Manhattan. However this is the mines in total.

If we consider just the city, it is likely no more than 2 miles long, and maybe a couple wide. Lets assume the city space occupies a square of size 2x2miles long. Taken into account the 7 levels and 7 deeps we get an area of about 56 sq miles. This is about 1.5x Manhattan, although this is counting each level as a separate space, without any "high-rise" buildings. Whether Moria has sub-levels and "floors" within levels is unknown