References:
Star Wars Technical Commentaries: Death Stars by Curtis Saxton (LINK)
Imperial Propulsion Technology by Michael Wong (LINK)

We'll start off with the Death Star II since there's more “physical” shots of it against things that can be used to get scale from.

Death Star II

Saxton's analysis (LINK) of the Death Star II has revealed different “known” diameters:

• Scaling off the curvature of the DSII's surface in the Executor crash in ROTJ: at least 1,000 km diameter.

• Scaling off the DS2 Equatorial Trench SFX shown in ROTJ: at least 800 km diameter.

• Scaling off the relative diameters of the DS2 and Endor: 900 ± 60 km.

Saxton also uncovered a statement by Richard Edlund of ILM from 1983:

“The Deathstar, I think, will be a lot more interesting than the one in the first Star Wars — mainly because it is under construction ... Plus, it will be MUCH bigger. In Star Wars, it was really difficult to establish the scale. It was supposed to be miles in diameter, but with a full sphere it was hard to tell. The NEW one is SUPPOSED TO BE MORE like FIVE HUNDRED MILES in diameter, but since we're not dealing with a sphere all the time, we'll e able to establish landmarks and get a better sense of scale.” – Richard Edlund of ILM, Cinefex Magazine, July 1983; pages 7-8.

For statute miles, that works out to a 804.6 km diameter. If nautical miles are used, the diameter is 926 km.

Adding up all these estimates gets us a median diameter of 900 km and an average diameter of 886.1 km. I tend to go with the 900 km diameter as it is “neater” from an Imperial engineering OCD point of view.

A 900 km diameter gives us a volume of 3.81E17 and a mass of 9.53E19 tonnes for the DSII at 250 kg/m3 density – that is, if the Death Star II was completed.

The Return of the Jedi novelization says it was only half completed. If we estimate 65% of tonnage for the DS2 was built/ordered before it's destruction, then it's economic impact was 6.19E19 tonnes.

Death Star I

Saxton has noted that in the famous Death Star Trench Run, the targeting computer(s) highest digit count is about 470xx, indicating a minimum trench run of 47~ km; which is far too long when compared with the “official” 120 km diameter of the first Death Star.

Death Star 1, Trench Run Targeting Computer showing 47~ km range to target.

We do have one useful hint from the Return of the Jedi novelization on the scale of the first Death Star, albeit indirectly:

At the feathered edge of the galaxy, the Death Star floated in stationary orbit above the green moon Endor—a moon whose mother planet had long since died of unknown cataclysm and disappeared into unknown realms. The Death Star was the Empire’s armored battle station, nearly twice as big as its predecessor, which Rebel forces had destroyed so many years before—nearly twice as big, but more than twice as powerful. Yet it was only half complete." -- ROTJ Novelization

If we assume the Second Death Star was 1.8 times bigger (“nearly twice as big”) and that it's diameter was 900 km, then the first Death Star had a 500 km diameter. This gives us a volume of 6.54E16 and a mass of 1.64E19 tonnes for the DSI at 250 kg/m3.

The Death Star Prototype(s)

There's one way we can neatly square the 120 km and 160 km “official” sizes with the actual Death Star figures as well as reconcile it with the fact that the first Death Star somehow took 20 years to build between Revenge of the Sith and A New Hope; while the second Death Star was substantially complete about four years after A New Hope.

It's clear that the “Death Star” shown in Revenge of the Sith is not the one from A New Hope – the Superlaser dish is just wrongly proportioned compared to the rest of the “Death Star”.

I believe that what we are seeing is the Engineering and Development (EMD) prototype leading up to the finished, completed Death Star shown in A New Hope.

There's a lot of issues to consider in designing and building the Death Star(s):

• It has to move fast enough to maneuver at sublight to clear obstacles in a solar system in reasonable time frames – clearing the gas giant Yavin's orbit to bring it to a firing angle on Yavin IV in A New Hope required sustained acceleration on the order of 100G (LINK).

• It has to move fast enough in hyperspace to cover the distance from Alderaan (a Core World) to Yavin (an Outer Rim System) fast enough to arrive relatively shortly at Yavin after our heroes do – Vader himself remarks that most of the events of ANH occurred during a single day: “This will be a day long remembered. It has seen the end of Kenobi; it will soon see the end of the Rebellion.”

• The entire integrated weapons system has to work on a tactically useful level – i.e. no “we can fire the superlaser, but then we can't go into hyperspace for another 12 hours, because we have to recharge our energy banks,” or “We fired the superlaser, now we can't fire it unless we refill our hypermatter reservoirs to above 65%.”

That's a lot to ask even at the lower levels – An Executor Class Star Dreadnought has 1.26E10 m3 of volume, even a low scale 120 km diameter prototype Death Star has 9.047E14 m3; or about 71,800~ times the volume of the Star Dreadnought.

So it's not unreasonable to imagine that the Imperial Corps of Engineers demanded that an EMD prototype be built first, to prove that everything could be reasonably achieved within the present achievable state of the art before they committed to building the full scale 500 km version; rather than risk being left with a gigantic white elephant.

Assuming a design/test/iterate cycle for a prototype takes about six years, you can easily fill the nineteen years between Revenge of the Sith and A New Hope with development – i.e. the first prototype proves we can move something that big through hyperspace. Following that success, we scrap it and build a slightly larger design (160km) that holds a single reactor superlaser to provide more information for Galen Erso's design team so they can make sure a lot of risk is retired well before the initial 500 km version is declared operational.

Another point that has to be made regarding the Death Star is that a large part of its viability as a terror weapon relies on surprise and shock effect.

In more conventional naval engineering, you can get away with the fact that when your new Terror-class Star Destroyer fires it's two bow Ion Cannons, the recoil from the weapons causes nearby shield generators to blow; because you can just issue a standing order that the bow cannons are not to be fired until the requisite Ship Alteration (SHIPALT) is completed, pending design approval six months down the road.

The Death Star can't get away with that. It has to work the first time and there's a lot of parameters (move, shoot, defend) that have to be met and validated before Tarkin takes it to Alderaan.

Building unarmed or conventionally armed prototypes, by the way, can also act as “cover” for the greater Death Star project. All you have to do is claim that they're potential tests for a mobile logistics facility capable of supporting an entire Sector Group (24 Star Destroyers and 1,600 other combat ships) for long duration in the middle of nowhere.

This can be used politically – i.e. all the money allocated for these “mobile logistics facilities” is spent in Core and Deep Core shipyards building components through cutouts; rather than spending it to build refineries and supply depots in the Outer Rim.

If we assume the first EMD Prototype was 120km, this gives us a volume of 9.04E14 and a mass of 1.81E17 tonnes at 200 kg/m3 (lower density than production Death Stars due to large amounts of equipment not installed).

For the second EMD prototype of 160 km, we get a volume of 2.14E15 and a mass of 4.28E17 tonnes.

Presumably, when the first EMD prototype was scrapped, about 60% of it's mass (1.08E17) was recycled or reworked into the second EMD prototype, so the total mass of the entire EMD program was 5E17 tonnes.

The second prototype likely was kept around as a “test mule” for development rather than recycled into raw components for the first Death Star, because of the need to run tests right up to the official commissioning date.

Total Materials Consumption

Overall the entire Death Star Program (EMD+DS1+DS2) consumed about 7.88E19 tonnes of material; against a theoretical total Imperial Fleet Mass of 4.96E15 tonnes (based off Star Destroyers constituting 14% of total fleet mass).

I believe that this disparity (on the order of 15,887 times more mass consumed in Death Stars vs Imperial Navy tonnage) is why the Imperial Naval Order of Battle only has 1.6~ million combat starships in 1,024 Sector Groups instead of the 5+ billion or so ships that tonnage analysis shows that it should have.