Volumetrics

Starship Volumetrics I
Starship Volumetrics II:  Chrono-Volumetrics
Starship Volumetrics III:  Crew Densities

Recommended Reading:
Volumetrics 101 by 'BHMM'

Quick Reference

• I. Introduction and Acknowledgements
• II.  How to Use the Chart
  • A.  Nomenclature
  • B.  Scales
  • C.  Provided Data
  • D.  Final Notes
• III.  The Volumetrics Chart
• IV. Starship Mass Data Explained
  • A.  Star Trek Ship Masses
    • 1.  Voyager and the Delta Flyer
    • 2.  The Constitution Class
      • a.  Gross Tons
      • b. The 190,000 Tonne Fallacy
    • 3.  The Kobayashi Maru
    • 4.  The Borg and Starship Hull Material Densities
    • 5.  Historical Trend?
  • B.  Star Wars Ship Masses
    • 1.  Comparison to Star Trek Densities
    • 2.  Comparison to Real Spacecraft
    • 3.  Canon Indicators
    • 4.  Conclusion
• V. Addenda
  • A.  Footnotes and Observations by Class
  • B.  Tips and Tricks for the DIY Volume Calculation Guy
    • 1.  SketchUp
    • 2.  Blender 

I. Introduction and Acknowledgements

Deriving volume estimates for the objects and spacecraft we see is a troublesome task, especially for curvy TNG-era Trek ships.  Even Star Destroyers, which are basically just pyramids, have enough extra features and notches to thwart all but the most skilled volume estimators.  While it would be virtually impossible to do by hand, though, it can be done quite well by computer.   Raytracing programs have been around for a long time, but as the technology and internet have improved the online CGI modeling community has grown and shared its models.  Hundreds of extraordinary meshes are available these days from the vigorous and talented modeling community, and a good many of them are of sci-fi ships.   

Since this page was originally conceived and created, the technology has come a long way.  Though free programs like POV-Ray have been around since the DOS era, there were limits to what it could do.  Thus using CGI models to get volume estimates required tools such as areavol for Lightwave, with the latter being a very expensive and professional product.   However, one can now do volumetric analysis without LightWave or any other expensive modeler. Google Sketchup has had a lot of starship models made for it.  And, with a volume plugin found here, you can get far better estimates of a ship's volume than you can by simply guessing at simpler shapes.  More adventurous folks can try their hand at Blender's unique interface and use of the volume calculation script found here.

 Any such estimates are obviously rough estimates only . . . a model is not the "real" thing, and variances will occur with even the best-looking mesh of polygons.  Indeed, lower-poly models may even be preferable, since high-detail models can have overlaps, leaks, and other issues that skew the results, though some of the higher-detail guys are the same ones who so kindly clean out the interior of their models.   Of course you don't want to go too undetailed . . . calculating the surface area of a perfect sphere will put you in the ballpark of the surface area of the hull of the Death Star, for instance.  However, as anyone who's seen Star Wars can tell you, the Death Star's surface isn't perfectly flat and featureless.   The level of detail on the model, then, can make a large difference in the results obtained.

The above having been said, any data from just about any model is going to be far superior to what someone could come up with on paper.

Masao Okasaki of the exquisite Starfleet Museum (Enterprise, the way it should've been) was kind enough to provide me with some of that data as originally compiled by Nob Akimoto, a poster to the TrekBBS, using 3D Studio Max software.  The volume and surface area measurements were based on meshes whose design length corresponds to the ship lengths given by Bernd Schneider's Ex Astris Scientia starship database.   In addition, reader "D-Five" has also provided an amazing amount of LightWave assistance with this page, including providing some data for Star Wars vessels, confirming many of Nob Akimoto's values within a reasonable margin of variability.  (An exception was the Excelsior, which based on comparison with the TMP Constitution was simply too small in the Akimoto list; its data has been replaced below.)   The TMP nacelle information comes from "The Red Admiral".   And, yours truly has done a lot of work based on Google SketchUp and related models.

II.  How to Use the Chart

A.  Nomenclature

To save space, I've used abbreviations where appropriate.

Also, you'll see after certain vessel classes that appear more than once an A or B.   This is based on Captain Picard's use of the term "B-type Warbird", which happened to coincide with the first appearance of the second Warbird studio model, which had different features from the first.   This also works nicely given that the Enterprise-B is the first known vessel of the modified Excelsior class (with the secondary hull 'wing' additions and so on), meaning that the B-type Excelsior refers to the Enterprise-B, as well as merely referring to a second type of Excelsior.

As a result, obviously, the A-type Constitution is the TOS vessel.  The B-type Constitution is the TMP (movies) version.  The parallel universe ship from the 2009 movie onwards is referred to here as the Monsterprise of the Alt-stitution Class.  (No hate . . . it's just a huge ugly ship and easier to distinguish that way.)

B.  Scales

For the most part, the lengths of ships correspond to EAS, but there have been a few occasions where I made a judgement call based either on my own scalings or on choosing a different compromise of contradictory scalings than Bernd.  The important thing, however, is the model shape, since (if you've read Volumetrics 101) you know that it's a simple matter to get a new volume when length is adjusted.

C.  Provided Data

In the following, I provide the aforementioned length estimates along with the surface area and volume data for ships of that size and design.  Again, these are approximations only, and unless specifically marked otherwise I consider the ships to be valid representations and thus the values should be within a few percentage points.   However, your cubic meterage may vary.

Also provided is the surface area for some of the ships, to give a sense of the hull area.  That said, I'm not sure how detailed some of the other starship meshes were, which might affect the surface area part of the table somewhat.  For instance, the TOS Constitution is almost invariably modelled with a very smooth surface (much like the original filming models), whereas one might wish to put every little odd giblet, nook, and cranny from the Intrepid sensor suites on one's Intrepid model, which could significantly drive up the ship's surface area.   Thus, I wouldn't suggest trying to be too precise when drawing comparisons between the surface area of two different ships.

To my knowledge, Google SketchUp is not that useful for determining surface area of ships.  Thus, most SketchUp vessels are not represented with surface area numbers.

I also provide some other extraneous minutiae.  The first bit of minutiae is listed as "Venator Volume", and is intended as a comparison to the volume of the Venator Class Star Destroyer seen in Revenge of the Sith and extensively in The Clone Wars, having become for me the most familiar Star Destroyer.  Next comes a comparison to the Constitution Class (TOS) ship in multiples of the 1701 volume.   The same is done for the Falcon, rounding out a decent comparison set against better-known vessels.

There is also the volume coefficient, suggested in the Volumetrics 101 article by BHMM.  It is basically a comparison of the ship's true volume with a cube of the same length, so long skinny-looking ships will have a low one and wide, tall, beefy-looking ships will have a high one.  Then we have "V/SA" and the reverse, which gives a comparison value between the volume and surface area of the vessels . . . not all that useful necessarily, and I may drop it if I don't see a use for it soon.

And finally, I offer an estimated metric tonnage, based on the starship volumes and comparison with known tonnage.   The Star Trek values are based on statements of mass of Constitution Class and Intrepid Class ships, which due to very different densities serve as an upper and lower range based off two mass statements.   More on this very interesting data can be found here.  I'm also providing rough estimates for Star Wars vessel masses, rounded.  These are based on calculations and data explained in more detail here.

D.  Final Notes

Star Wars vessel data appears at the top of the list.  First come the two Death Stars, then other vessels in rough size order, listed by popularly accepted name.   Next comes Federation starship data, listed in order by popularly accepted class names.  Then come shuttles, stations, and adversary ships.  

There is some symbology below.  Vessels with a "~" in front of their values are based on models I find to be very questionable representations, such as my use of sphere data for the Death Stars.  Asterisk-laden class/vessel names are using values from the original Nob Akimoto TrekBBS data.

Note links precede many of the class names for more explanation and commentary, and links to SketchUp models are given where applicable. 

Where necessary, I have rounded the volume comparison numbers to keep the number of characters down and the colums small, so larger numbers have fewer digits after the decimal or none at all.  Also, I've used a sort of scientific notation for larger numbers, using "E6" and E9" to refer to millions and billions, respectively, rather than using varying powers (e.g. E8, et cetera).  Seemed simpler.

So, without further ado:

III.  The Volumetrics Chart

IV. Starship Mass Data Explained

A.  Star Trek Ship Masses

We know a few important things about various ships, some of which is useful.

1.  Voyager and the Delta Flyer

"The man drives a 700,000 ton starship, so someone thinks he'd make a good field medic." 
            - The Doctor, "Phage"[VOY1]

"700,000 metric tons, 15 decks, computer systems augmented with bioneural circuitry, top cruising speed warp 9.975."
            - Captain Janeway, "Relativity"[VOY5]

The first, smaller masses in the list above were obtained from dividing the 700,000 tons by Voyager's volume, and then applying that density to all the other ship volumes.   The result of the division was approximately 1.11842, which implies that the density of the Intrepid Class starship should be just 1,118.42 kg/m³, roughly (and intentionally) corresponding to the density of the Apollo capsules per TrekBBS posts by Rick Sternbach.  

A similar density for the Delta Flyer can be derived from "Thirty Days"[VOY5].   The Delta Flyer is used to go to the center of an artificially-maintained water sphere in space.   The center is said to be over 600km deep, and the residents of the water sphere have never gone there due to the pressure.    The Delta Flyer goes down there easily, but loses immersion shields and propulsion and thus must float back up.

Can the water density at such a depth be determined, thus giving us some indication of the Flyer's density?  There are possibilities.   The water sphere had a device in the center which somehow offered containment via artificial gravity.  Whether this acted like a natural gravity well or projected a containment field at the surface is unclear.  Assuming it was the latter, though, we can make some very rough calculations.  A 1200km sphere of water will mass approximately 9.05E20kg, or about 1/6600th of Earth's mass.  The sphere should thus have a surface gravity of about 0.16773 m/s, so at a depth of 600km the pressure would be about 100 megapascals, or almost a thousand times normal Earth atmospheric pressure.  This is roughly equivalent to the pressure at about ten kilometers below sea level on Earth (and it doesn't get much deeper).  At such a pressure, the density of water becomes higher, approaching 1100 kg/m³.   To float back up, the Flyer had to rid itself of non-essential equipment . . . this might suggest that the flyer's normal density is probably similar to that of Voyager.

If, on the other hand, the central containment device acted more like a normal gravity well, then based on a simple depth model of our own ocean at 30 degrees latitude, even a chilly 100km depth would've produced a water density of over 1300 kg/m³, and a pressure of 1,500 megapascals..

Those two values serve as very rough lower and upper bounds for the Flyer's density.  It isn't clear, though, whether these values would work for other shuttlecraft . . . the Flyer has several Borg-inspired systems, a hull composed of tetraburnium instead of the normal tritanium or duranium, and so on.   However, it is nonetheless a potential supporting fact.

2.  The Constitution Class

The second, larger masses in the table above used a similar method based on a different comment altogether:

"Almost a million gross tons of vessel, depending on a hunk of crystal the size of my fist."
            - Chief Engineer Montgomery Scott, "Mudd's Women"[TOS1]

a.  Gross Tons

Scotty's statement is a curious one . . . gross tonnage generally isn't a unit of mass at all in the naval context.  The best jargon-free definition would be the one I found here, where the following is stated:

 "A Gross ton is not, as some would expect, a unit of weight.  Rather it is a marine term equal to 100 cubic feet [...] used to describe the size of vessel.  Gross tonnage indicates the internal volume of a vessel, including cargo holds and other areas, while net tonnage is the commercially useful internal capacity of the ship, that is, gross tonnage less the crew quarters, engine rooms, and so on."

As noted above, the volume of the ship is estimated to be 211,248 cubic meters.  That's 7,460,152 cubic feet.   The ship should therefore be about 74,600 gross tons, not even close to "nearly a million".   

One solution would be to accept Scotty's statement and take the ship to be a helluva lot bigger . . . but we can't do that.   Not only do we get a good sense of the ship's scale from the windows, the TMP hull-walking scene, various comparative graphics (such as the one in Keiko's classroom on DS9) and so on, but we also have a direct sizing of the ship (in feet) from "The Enterprise Incident"[TOS2]:

(Thanks to Trek5 for these images)

There's just no way the ship should be ballooned out to the length that would be required to give her nearly a million gross tons of volume.  The images above constrain us to the low-to-mid 900s, in feet . . . or around 289 meters.   Had Scotty meant to imply that the volume-based gross tonnage were about 900,000, then the ship would have 900,000,000 cubic feet of volume.  That's 25,485,161.9 cubic meters.   Using the volume coefficient based on 289 meters and 211,248m³, then the Constitution Class would have to come in at 1,428 meters, or over 4,700 feet.  That's well above any estimate for the vessel, and given Picard's direct statement that the Enterprise-E was almost 700 meters long, it would put the Constitution at over twice the length of the Sovereign Class.  Obviously taking the gross tonnage as a volume statement is not the way to go.

There is, however, a solution.  The Imperial weight scheme features the "gross hundredweight" or "long hundredweight".  Twenty of these are equal to a "gross ton" or (as it is more commonly known) a "long ton", equal to 2,240 pounds (1,016kg).  References here, here, here, et cetera.   

Besides serving as an argument for the immediate adoption of the metric system in both normal and naval affairs to avoid all this damned confusion of similar terms having totally different meanings, this also happens to mean that Scotty's statement was not in error.  The Enterprise was indeed nearly a million gross (or long) tons in mass.   If we assumed that "nearly a million" equalled 900,000 gross tons, then the ship's mass would be 914,442 metric tonnes, and her density would be 4,329kg/m³.

b. The 190,000 Tonne Fallacy

The Star Trek non-canon has featured different mass estimates for NCC-1701.  One of the more popular has been a figure of 190,000 metric tonnes, which originally appeared in the writer's guide (much like a 1.5 million tonne figure for Voyager).  The 190,000 tonne figure, however, appeared well before the design of the ship was finalized, and before a final size had been chosen.   (One of the early Enterprise concepts had the ship as being 200 feet long, and even shortly before the first pilot the ship was thought to be around 500 feet long.)   

Nonetheless the figure persisted, due in part to its inclusion in Whitfield's 1968 "The Making of Star Trek" which made it easy to find and reference in an age before DVDs and VCRs.   From there it made its way into Franz Joseph's Technical Manual, and from there into many other materials.  Some newer non-canon materials such as the DS9TM have supported the canon mass by showing TMP-era vessels as having high densities, but others such as Starship Spotter continue to use the fandom figure.

At 190,000 tonnes, the TOS Enterprise would be 90% as dense as water . . . that is to say, the ship would float.  Voyager, a ship designed to land and which is explicitly identified as being fast and nimble, would be 133% denser.   That's 136,000 metric tonnes extra.  This, of course, makes little sense . . . one would expect Voyager to be as light as possible, with probably the smallest density in the fleet.  Otherwise they could just slap landing legs (or pontoons, for that matter) on an old Miranda class and go on about their business. There's also the oddity of the idea of the Enterprise being only 75% as dense as the Apollo command modules.

Some proponents of Trek fandom deride Scotty's canon comment as "anomalous".   Others claim that Scotty was engaged in hyperbole (albeit a minimal example) because, they say, he was exasperated.   In general, such 'fandom-boys' claim priority due to 35+ years of non-canon materials which have persisted with the erroneous figure.  Further, it's claimed that the "Mudd's Women" statement was an error by the writer, listed in the credits as Stephen Kandel, and it's also claimed that Roddenberry personally reviewed the Franz Joseph repetition of the writer's guide figure and signed off on it.

Such arguments are flawed in multiple ways.  First,  the lone canon example from TOS is not an anomaly, by definition, since there is nothing canon to compare it to.   Second, Scotty's tone and demeanor . . . not to mention the reaction of Kirk and Spock . . . hardly qualifies the statement as one of Scotty freaking out and exaggerating things.   See the behavior here:

Third, an error that persists does not become more correct the longer it lasts.  It simply becomes an older, more oft-repeated error.   Given that the mass is stated in the show as "almost a million gross tons", it is rather silly to then claim 190,000 tonnes. This would be like deciding Voyager's mass was 1.5 million tonnes (as per the writer's guide) despite clear contrary statements in the show. It just doesn't happen for the 90's show, so why would one do it for the 60's show?

Finally, the TOS writers did not operate in a vacuum . . . Roddenberry's rewrites and the oversight by the writing team (with occasional input from Rand engineers) were well-known.   Further, as reported in Star Trek Creator (p. 285), the writing credits submitted to the Writer's Guild for "Mudd's Women" read "Story by Gene Roddenberry; teleplay by Stephen Kandel, John D.F. Black, Gene Roddenberry".  Roddenberry also attempted to charge Desilu for a "polish" of the story.  Thus, there is no question on the matter of authorship and validity . . . Roddenberry was directly involved in the script which described the ship as being almost a million gross tons.

3.  The Kobayashi Maru

There has been one other incident wherein we received detailed ship data, though it has too many problems to be very useful.  Note the following graphic from Star Trek II:

As you can see, a freighter of that period could mass at least 147,943 metric tons, or 147,943,000 kilograms, when loaded.   Unfortunately, we don't know anything about the ship's volume.   We have the length, width, and height, but that has little meaning.   Only the Borg make ships which are blocky enough to actually fill a box based on their length, width, and height.

Add to that the fact that we have a situation not unlike the "gross tons" above.   "Dead Weight Tonnage" doesn't refer to the mass of the ship, though this is a common misconception.  It actually refers to the difference in mass between a ship when fully loaded and when empty. However, since we also have the cargo capacity in metric tons, this seems a peculiar redundancy, and given the difference of 50,000 metric tons it also would seem to be a peculiar discrepancy.  On the other hand, the additional 50,943 metric tons (over and above the cargo) could refer to ship's additional operating equipment, stores, the 300 passengers and their effects, the 81 crew and their effects, deuterium, and so on . . . even though that seems like an awful lot. It does not refer to the superstructure, propulsion systems, and so on, if it really is dead weight tonnage. In any case, using the 147,943 metric ton figure as ship's mass is actually quite conservative, since that figure (if used properly) would not include the actual mass of the ship, but simply the mass of cargo, personnel, et cetera. The actual mass of the ship when loaded would be far greater.

Still, the main problem with the Kobayashi Maru . . . besides being fictitious, even in the fictitious Trek universe . . . is that we never get to see the design of the ship.   Is it really a 237 x 111 x 70 box?   Or is it a 237 meter long, two-meter wide cylinder with some slender 34 meter long appendages on the top and bottom, and some slender 54.5 meter long appendages on the side?   We have no way to know.  As a result, all we can do is guess at the density of the ship.

4.  The Borg and Starship Hull Material Densities

In "I, Borg"[TNG5], the Enterprise discovers a crashed Borg scout vessel.  Riker, Worf, and Crusher beam down and find a Borg cube that appears to be approximately the size of a small house.  Only one of the five crew survived.  

Later, what Data describes as "a scout ship similar to the one that crashed" comes to the area to find the crashed ship.   Data reads its mass as 2.5 million tonnes.   Even if we assume that the crashed vessel is much bigger than what we saw on the planet . . . some buried in rock or spread around elsewhere on the surface . . . the small crew does place certain limits on its size given normal Borg crew densities.

But at 2.5 million metric tons, the ship would have a mass over three times that of Voyager.   Unless we try to make the ship ridiculously large, this must imply a very high density.

We know from "Endgame"[VOY7] that Borg hulls use tritanium, and this is also used for the infrastructure of their tactical drones ("Dark Frontier"[VOY5]).   

What else do we know of tritanium?   Well, we also know that natural veins of tritanium ore are 21.4 times as hard as diamond and well-nigh impossible to break ("Obsession"[TOS]) and virtually impossible to melt ("Arsenal of Freedom"[TNG2]).  (This naturally leads one to wonder how the hell they do anything with it, but that's neither here nor there.)    We know that the material can be alloyed with various other substances ("Dead Stop"[ENT2], "The Raven"[VOY4], et cetera).   Tritanium alloy is commonly employed in starship framework/hulls ("Dead Stop"[ENT2]), ship hulls ("The Raven"[VOY4], and Type-6 shuttle hulls ("Rascals"[TNG5]).  The interior bulkheads of the Enterprise-D are also tritanium in some cases ("Where Silence Has Lease"[TNG2]).

The Borg ship density would imply that tritanium is very dense.

Also featured on ship hulls is duranium.   The outer hull of NX Class ships was lined with duranium in the 2150's ("The Xindi"[ENT3]) as insulation.  Duranium was used for the outer shielding of the warp core on Intrepid Class ships, and would require a sustained phaser beam to burn through ("Projections"[VOY2]).   Duranium alloy was considered for reinforcement of the tritanium shuttle hull in "Threshold"[VOY2], but was thought to be too brittle for the purpose of transwarp.  The hull of Voyager is at least partially duranium ("Drone"[VOY5], "The Disease"[VOY5]).  Duranium was added at some point to reinforce the hull of the tetraburnium-hulled Delta Flyer ("Body and Soul"[VOY7]), hence the reading of duranium alloys in "Once Upon a Time"[VOY5].  

Cardassian Nor-type stations use two-meter thick duranium composite in the construction of their access conduits, making them difficult to scan within ("Captive Pursuit"[DSN1], "The Siege"[DSN2]).  Duranium composite is also used for the rather less-thick hatch doors of Federation runabouts.  Sisko estimated that it would take Kira an hour to burn through it with her Bajoran hand phaser ("Q-Less"[DSN1]).  Duranium alloy from a destroyed Klingon Vor'Cha cruiser's secondary hull had a magnetic field sufficiently strong to partially disrupt runabout sensors ("Dramatis Personae"[DSN1]).  Magnasite in a liquid form is a substance that can eat through the duranium pins used to hold panels on the walls of DS9 ("Necessary Evil"[DSN2]).  "Poly-duranium alloy blend" is used on the bridges of Defiant Class ships.  Gallamites were trading partners with the Federation, supplying duranium for the war effort ("Penumbra"[DSN7]).

Corridor panels on the Enterprise-D were solid duranium ("A Matter of Perspective"[TNG4]).  Simple transporter test articles were made of solid duranium ("Hollow Pursuits"[TNG5]).   TOS shuttle hulls were a duranium metal shell ("The Menagerie"[TOS1]).  "Most shuttlecraft hulls are made of duranium", according to Geordi in "Final Mission"[TNG5].  Data's skull is partially composed of duranium ("The Chase"[TNG]).  

For the most part, these datapoints would seem to support the idea that duranium is rather light, and features pleasing thermal conductivity properties.

5.  Historical Trend?

Based on the density difference between Voyager and the Enterprise, it's possible that starship densities decline as time goes by, presumably due to design improvements, metallurgical advances, and of course technological advances in propulsion systems.

Granted, it's dangerous to theorize like this with only two data points, since there are plenty of factors which would affect a ship's mass and plenty of other differences to look at in regards to the two ships.  Intrepids, for instance, have tiny nacelles compared to the Constitutions.  Voyager's nacelles account for less than six percent of the ship's total volume, whereas the TOS-era Constitution nacelles account for over a quarter of the Enterprise's volume.  (The Galaxies, incidentally, feature nacelles just under ten percent of the volume of the ship.)  The weight distribution suggested by Voyager's landing legs would seem to go along with the idea that warp nacelles are very massive objects, meaning that the overall density of the Constitution Class Starship may be centered in the area of the nacelles.

Also, the datapoints above regarding hull material densities might also be a clue.   Most starships have been referred to as having tritanium hulls, whereas Voyager's hull is apparently duranium.   Of course, it's most likely that, as is the case with NX-01, both materials are present to some degree.  However, if Voyager's hull is low in the dense tritanium (or if the tritanium is virtually absent from her hull), then it could be that much weight was shed in the design process by giving her a less-dense (but probably more thermally insulated) hull.

Then, there is the ship itself.   A larger ship will require increases in hull materials and internal structural members that will, as a rule of thumb, increase the vessel's mass far beyond what simple scaling by length would suggest.   If you draw a square 10 centimeters in width, a second square of 20 centimeters in width can easily be seen to have four times the surface area, despite the fact that you only doubled the width.  Volume works the same way, only it cubes instead of squares . . . a 10cm cube has a volume of 1,000cm³, whereas a 20cm cube has a volume of 8,000cm³, and a 30cm cube is 27,000cm³!   The surface areas of the cubes do not rise so quickly . . . 600m², 2,400m², and 5,400m², respectively.   But, if the ship's hull and superstructure are some of the most massive parts of the vessel, it's easy to see how quickly the mass of the ship would increase if the ship were larger but built to withstand the same sorts of forces.

B.  Star Wars Ship Masses

While working on an old unfinished page I'd forgotten about, I realized that I really needed a decent estimate of Star Destroyer mass.   Despite not having much to really go on, I decided to make a guesstimate.   Unless and until we get more information, it's as good as anything else, if not better.

So, let us assume that a Star Destroyer is 1600 meters in length.   Now we need an estimate of the density.   We have options here.

1.  Comparison to Star Trek Densities

We can attempt to use the density of Star Trek vessels.  Something similar to this move was performed by Mike Wong when estimating the density of the Millenium Falcon, basing his Falcon mass off of a simple volume estimation and the Star Trek TNG Technical Manual mass for the Galaxy Class Enterprise-D, plus an unknown volume estimate of that ship.  We can do a much better job of this, though, with canon data and more advanced volumetrics.

Star Trek vessels like the Intrepid Class, for instance, have a density of over 1100 kg/m³.  However, we know that the vessels are constructed of different materials and so on, so this is a somewhat dangerous assumption.  There's also the fact that the Constitution Class ships had a far higher density of over 4300 kg/m³.   However, given that the Intrepid can land as most Star Destroyer classes seem able to, the Intrepid density seems the safer (albeit still dangerous) assumption.   So this would suggest  1100 kg/m³. 

2.  Comparison to Real Spacecraft

We can attempt to use the density of real-world spacecraft.   This is also dangerous, of course, since real-world spacecraft are hardly military vessels.  They are designed to allow people to get to space for a brief period of time, but can hardly be expected to withstand even a single hostile bullet or other decent-velocity impact.

Now, it happens that when Star Trek guru Rick Sternbach was designing the Intrepid Class for Star Trek: Voyager, he intentionally based their stated mass off of an estimate of the ship's volume, calculating the mass via a density derived from an estimate of the Apollo capsule command module.  And indeed, the Intrepid density is within about 10-20% of that value, assuming the Intrepid model used on this site for the estimate is basically the same as his.   However, the command module was basically just the crew compartment and heat shield for re-entry, a single part of the combined Command/Service Module (CSM), with the service module featuring the large engine bell and other machinery that enabled Earth-Moon transit.

Taking that combined vehicle massing 30 tonnes and estimating her volume based on this Google SketchUp model (with or without engine bell) results in a CSM volume of approximately 80m³.   Prior eyeball estimation based on a 4m diameter and 8m length, with 3 of her 11 meters removed to account for the engine bell and conical front, suggested a volume of 100m³.  However, with just the bell gone the total CSM length is 8.5 meters, meaning prior eyeball estimation was off significantly.   Thus, 30,332 kilograms divided by 79.9 cubic meters gives us 379.6kg/m³ as the approximate vehicle density.  However, given that we are counting the engine bell as part of the ship's mass without accounting for its volume, it may be beneficial to report the overestimated volume's density reading of  298kg/m³, as well, to give a sense of potential upper and lower values.

That seems a bit light, so we can also compare to the space shuttle orbiter.  Empty, a newer shuttle like Endeavour weighs about 70 tonnes, and she's about 105 tonnes when full.   At about 37.25m long, 23.75m wide, and 17.25 meters tall, she's a big girl.   Determining her density is a little bit of a trick, though, since much of her total empty mass . . . not to mention her width and height . . . is nothing more than wing surfaces and structure, not to mention her big empty cargo bay.   But since we're ballparking, we can simply take the fuselage as a cylinder and guesstimate that her wings surfaces could be crushed to fit into the cargo bay.

So, per estimation from this site, we have the total length of 37.25 meters.   A smidgen of that is the vertical stablizer (the tail fin), but we'll just roll with that figure.  Given that the shuttle fuselage is roughly cylindrical, the height and width values of about 6 meters are sufficient for diameter (the crew area and payload bay are below six meters, the rear fuselage with the engines is over six).   So if we ballpark a 35x6 cylinder, we come up with a total volume of 990m³.  Alternately, we can take this SketchUp model and, adjusting the size, get a volume plug-in result of 827m³ . . . a big difference, but not critical for our purposes.

Given her empty and full masses, the density ranges between 71 and 106kg/m³ for the eyeball modeling, or 85 to 127kg/m³ for the SketchUp version.

3.  Canon Indicators

Given the extensive use of simple steel even for external towers on the Death Star (per the ANH novelization), Coruscant buildings, and similar, it seems unlikely that durasteel or steelcrete will be superdense.  Even the Invisible Hand used "hydrofoamed permacrete to save weight" for some of its walls and bulkheads.   And of course, given that a natural stone on Yavin was so dense that no weapon was thought capable of penetrating it, we could be forgiven in believing that Star Wars ships are built strong but as light as possible.

That said, the space shuttle is framed with aluminum for much of it, and most modern spacecraft are, again, basically built like tin cans.  But interestingly, both the shuttle and vessels of the Clone Wars era are built with big empty spaces.  For instance,Venators with their extensive landing bay areas, the Malevolence with its massive open center railway areas, and so on . . . and the Death Stars seem little different in that regard.

4.  Conclusion

 It seems that Rick Sternbach's choice was rather on the heavy side compared to other real spacecraft.  The space shuttle tops out at around 125kg/m³, the Apollo CSM 400kg/m³, and the Apollo command module with heat shield by itself is near 1000kg/m³.  And yet the Constitution Class still came in four times more dense than that, and a couple of dozen times denser than the space shuttle!

So where should we attempt to put the Star Destroyers?   Considering that large warships of the Clone Wars era seem to be largely hollow even more than we might expect for simple hallways and such, I hardly feel comfortable comparing it to an Intrepid Class ship that has very little empty space by comparison.  But I also don't want to compare it to a tin can.

That said, I figure Star Destroyer density probably falls somewhere in the 500-1000kg/m³ range.

Given a calculated volume of about 54,000,000m³ for Star Destroyers at 1600m length, and a density range of 500-1000kg/m³, the mass of a Star Destroyer should fall somewhere between 27,000,000,000 and 54,000,000,000 kilograms.   That's 27 to 54 million metric tonnes.  

If one wants a specific estimate, I'd guess a density of 750kg/m³ and an ISD mass of 40,000,000 tonnes.  However, for the purposes of the above chart, we'll give the full range.

V. Addenda

A.  Footnotes and Observations by Class

In no particular order:

0.  The Death Star estimates are heavily rounded above, because they're for simple spheres (i.e. not counting trenches, superlasers, surface emplacements, and so on).  But as big as the bloody things are, do we really care?  We could lose the equivalent of tens of thousands of Star Destroyers as a part of rounding off and not notice.

That said, a pretty cool SketchUp model with interior details visible (fun to play around with if nothing else) is here.

1.  The Sovereign's length (and volume, as well) changed in between Insurrection and Nemesis.   The CGI model was heavily reworked, and basic details -- nacelle position, pylon angle and thickness, and keel structure -- were significantly and visibly altered.  

Similar issues would occur with other "star" ships, such as the TOS Enterprise, Enterprise-D and the Defiant.    In the case of the Enterprise-D, there was the slender ILM six-foot Enterprise-D, or the thicker "Bulldog" four-foot Enterprise-D built by Greg Jein.  There were also multiple Defiant models, from the main physical model to separate and dissimilar CGI models by VisionArt, ILM, and Digital Muse.  The VisionArt versions were very close to the model, and very high quality.   The ILM version built for First Contact was quite good, as well.  Then there was the butt-ugly, long-nosed Digital Muse model (used to represent the USS Valiant, as well as the Defiant when she appeared in "Sacrifice of Angels").   

In the case of the Sovereign, we have to assume a refit occurred.   However, the Galaxy and Defiant ships which would switch back and forth even within the same episode (thanks to the magic of stock footage) have to be assumed to be the same, even though we know otherwise . . . unless we want to assume mid-episode refits or inflatable hulls.

2.  I agree with the EAS 120 meter length for the Defiant, even though the official line is that she's 170 meters in length.   The vast majority of visuals support a ~120 meter length for the ship.   (Scaling anything from DS9 can be a little tricky, however, since David Stipes chose to scale things at his dramaturgic whim, while also maintaining a length list with extremely peculiar values on it, to say the least.  I do not hold his work in high regard as a result.  I bet he liked the Big-Nosed Defiant, too.)   More details on size and scaling issues are available in the EAS Starship Articles section.

A Sketchup model here is not perfectly accurate (it appears to be based on the Star Trek Fact Files inaccurate rendition of the ship), but nonetheless the volume comes out to about 61,150 cubic meters when calculated at 5%.  That's within tolerances.  Another model here looks pretty good, except for the slender nose and possibly a too-wide main hull.   Don't bother using the second model for volume work . . . it reads a third of what it should.

Remarkably, the Defiant is 1/16th as voluminous as the Excelsior-B Class Lakota, yet in "Paradise Lost'[DSN] the two fought to a rough draw.  The Lakota had been holding back, fighting to disable the Defiant and thus not using quantum torpedoes, but the Lakota was also in very bad condition, with the Defiant crew believing her to be one good hit away from being "finished", killing everyone aboard.   To be sure, shooting to disable increased the degree of difficulty for the Lakota, but it is still remarkable that the Defiant held up.

3.  I'm presuming that the Nebula is of the standard type (the "Sutherland" edition, seen throughout DS9), and not the version with the Phoenix "AWACS" pod, which was a longer vessel.

4.  The Galaxy Stardrive refers to the entire Stardrive section . . . the engineering hull and warp engines as seen when the Enterprise-D separates, which by volume is about one third of the combined ship.   I have no idea what the masses are for the separate parts, but it appears that nacelles should be heavier.  So, take the mass figures for the separated ship with the suitable grains of salt.

Interestingly, the Stardrive alone, minus the nacelles, is by volume worth 9.2 Constitutions, minus nacelles.   But, she's only worth 1.9 Excelsiors-sans-nacelles.  For the Stardrive plus Saucer but still minus nacelles, the figures are 33.8 and almost exactly 7.

The Galaxy Class USS Odyssey, without shields, was forced to withdraw by three Jem'Hadar attack ships.  That should give a sense of the technology level and combat-oriented nature of the Jem'Hadar ships, given that by volume the Galaxy should've outmatched the bugs well over 100 to 1.

5.  As noted, nacelles are thought to be the densest part of the ship.   As such, nacelle masses (previously simply not calculated) are here darkened a bit.  I do not think they should be used for most purposes.  For instance, in the case of the TOS and TMP era ships, nacelle mass might very well surpass what is listed for the higher end simply because the high end is calculated based on the complete mass of an entire TOS ship.  In any case, I leave the figures available merely for interest.

6.  The Jem'Hadar attack ship data is considered to be more of a guesstimate than an estimate.   The model of the ship available online resembles the bugs, but is by far the least-accurate model used in the chart above.

7.  The Tac-Fighter is the fighter used by Starfleet and the Maquis . . . it is not the "Maquis Raider" or the Peregrine.   The full-size raider is the Antares Class, as named in Pathways.  The smaller version used by the Maquis is the Peregrine Class "courier ship", as Odo describes in "Heart of Stone"[DS9-3].

Everyone calls the Federation fighter the Peregrine.  I kinda like that name, too, even though I'm credited at EAS with the counterargument (from here originally).  Oops.  But, then, it's not my fault the writers associated the name Peregrine with a courier ship instead of a fighter.   Oh well, whichever.  In any case, here's the externally lovely model used, converted to SketchUp and with the interior cleaned up by yours truly.  Just a note . . . unless the fighter has more room than indicated by its Type 15 shuttlepod cabin (e.g. unless there's some way to 'go below' or a bed behind the cabin or something), the fighter probably has a higher mass than we might expect, given that whereas shuttlecraft are large and empty on the inside, the fighter must be crammed almost full of stuff by comparison.  I'd imagine it probably rivals the Delta Flyer's mass.

8.  Deep Space Nine's width is, in the final analysis, a best guess.  DS9's David Stipes liked to rescale things for "dramatic" reasons (i.e. laziness), which is why the station, originally designed at 1,097 meters, is sometimes scaled as high as two kilometers and sometimes scaled as low as 335 meters (1,097 feet) compared to the little spacesuited guys in the credits.  The DS9 Tech Manual suggests a compromise of 1,451 meters, but I don't see that as particularly helpful.   Comparing the station to a 120 meter Defiant, the runabouts on the pad, the Galaxy dockings, and so on, a figure around 1300 meters seems to work the best in my view.

Here is a very pretty SketchUp model, though the Promenade windows are way too big.  I had great trouble at first getting the volume from it . . . it gave almost 100,000,000 cubic meters.   I knew this wasn't right, both because of the earlier LightWave model volume and a more basic approach.  For instance, the station model is 56m thick at the outer docking ring. If we assume that all of the station's material could be squished into a cylinder of the DS9TM diameter by 15m height, which seems more or less right by eyeball estimation, then we'd wind up with a figure of 24,779,464 cubic meters. That's pretty close to the existing value I had for the station at 1250 meters.  So a figure four times that was right out.

I finally determined that the volume estimator plug-in was having great trouble with the ring shape of the station, inserting volume estimation planes right across the empty interior pieces of the station (i.e. making it a disk rather than a ring).   Turning the station on its side cures this problem.

I went ahead and gave mass values for DS9, even though it isn't a starship and is without the heavy nacelles.  On the other hand, the station has two-meter thick duranium around some of its conduits ("Captive Pursuit"[DS9-1]), so I figure the mass should indeed fall somewhere in that range.

Incidentally, the station was, as of "Sanctuary"[DS9-2], only capable of housing 7,000 people according to Odo.  By the time of "Field of Fire"[DS9-7], over 900 Starfleet personnel were aboard.

9.  The Klingon Bird-of-Prey has similar scaling issues to DS9, having been scaled at everything from 50 to over 700 meters in various scenes throughout Trek.   We know there are various classes of the ship, though, which gives a little wiggle room.   In the above, I assigned the canon names to reasonably-average canon sizes.   The ship's volume, incidentally, will change a bit depending on the wing configuration . . . both BOPs were measured with wings flat, not tilted up or down.   Your mileage (or meterage) may vary.

Here's a decent-looking Google SketchUp model, but the ship's got some weird gaps in it (e.g. between the top and bottom halves of the two main hulls), so its volume reading is considered less accurate.

The Bird-of-Prey is also the source of a unique objection to this page, in that it is claimed that the BoP from Star Trek IV was floating or at least partially floating in the San Francisco Bay.   This is incorrect.   The central San Francisco Bay has an average depth of 13.4 meters, or about as tall as the 110m BoP head section, which was sitting at an angle out of the water.   That actually makes a lot of sense for a Bird-of-Prey in flight mode that has had its tail sink in shallow water.  As such, there's no reason to assume that the Bird-of-Prey did anything else but sink her butt into the mud right away.

10.  The Jem'Hadar battlecruiser is commonly estimated to be something like 600-650 meters.   However, scrutiny of its first appearance in "In Purgatory's Shadow"[DS9-5] and close comparison to the attack ship shows that the vessels simply cannot be that large, at least in that episode.  I haven't seen enough of the later seasons to judge the ship's size later, though.

11.  Being a much shorter ship, one might've expected the Miranda to have much less volume than the Enterprise-A.   However, the large four-deck-high extension on the rear of the saucer does much to offset the issue, though that and the torpedo "roll bar" do cause the ship's surface area to be rather high (hence the low value for its V/SA ratio).   The same sort of thing occurs with the Nebula, whose pod severely increases the surface area while providing little volume, giving the total ship about half the V/SA of the Galaxy Class. 

12.   The original Warbird model as used on this site was a really crappy looking Lightwave model.  This SketchUp model is far superior in appearance, but leaky as hell.  As soon as I can get it repaired I'll be using its volume instead.

13.   It's interesting to see that there was such a sudden jump in ship volumes around the TMP era.  The Constellations and Excelsiors are both over three times as large as the Constitution.  To be fair, both have about twice the Constitution nacelle volume, thanks to the Constellations' four engines and the big huge engines of the Excelsiors. Still, though, the Excelsior A minus nacelles is 4.86 the volume of the Constitution A.  And the Excelsior (minus nacelles) is almost half again as voluminous as theConstellation (minus four Constitution B nacelles).

   It's also curious to note that the only other ship design of that era, the Soyuz Class, should also have an interior volume substantially greater than the Constitutions.

The Constellation Class was described by Picard as underpowered, though of course that was some 75 years after the initial appearance of the class, a class which was not seen upgraded as some Excelsiors were (e.g. the Lakota).

14.   The NX Class is disturbingly big compared to the Constitution.   She has about 94% of the volume of the Constitution, which is bad enough.  However, if you add to that the fact that her nacelles take up far less percentage of that volume, you come to realize that the useful internal volume of the NX Class is actually greater than that of the later Connie!

Fortunately, the NX has a crew of just 80 instead of the 203 of the 2250's Constitutions.  This allows us to assume that the ship's inner mechanics . . . propulsion, life support, et cetera . . . actually take up a far greater percentage of the available volume than on the later ships.   Nonetheless, a less-voluminous design (read: "Daedalus") would've been preferred.

15.  A SketchUp TOS Connie, when rescaled, comes out to 216,000 cubic meters. My ST-v-SW Connie volume is 211,000.  Given that the SketchUp volume plug-in has accuracy settings (in this case, 5%), that's pretty damn close, representing a difference of just over two percent.  I consider that more than close enough to consider the old Connie value confirmed. 

16.  The Super Star Destroyer model employed (via LightWave) was somewhat iffy.  But, then, the cityscape on the top is difficult to model correctly, and given its massive, voluminous bulk any tiny difference will show up as the equivalent of several smaller starships.  So, your mileage may vary here.  That said, however, this SketchUp model gives a very similar value at 12,955,000,000 or so.  I'm not worried because that's just a 2% difference . . . which is just scary, since that 2% is the equivalent of a few Star Destroyers.

17.  I had found several other Acclamator models before finally finding this excellent one that's light-years better than the others, at least in shape . . . who knew I needed to search for "Eclamator"?    I'd love to get a true count of troop carrying capacity.

18.  The ISD volume on this page was in error for a great long while, but is fixed now.  (I originally had 53,942,400.)  

You'll want to be careful of leaky or otherwise poorly finished Star Destroyer models, since for some reason Star Destroyer mesh makers are some of the worst in that regard.  Hand calculation can be tricky, too, given that it's tempting to simply calculate based on a pyramid for the main hull and assume that most of the bridge tower and superstructure can fit into the gaps.  But, even small variations in the proportion estimates can make for massive variations in the final product, and the Star Destroyers are frequently the topic of misinformation as to their proportions.  (See 18a below!)

This is why assorted hand calculations for the ISD volume (such as some at StarfleetJedi or even some on SDN (e.g. 55 million argued by Surlethe)) frequently appeared to confirm the old value.  So, when a SketchUp model here (one of my first uses of the plugin) read about 45 million cubic meters, and with many hand-calced estimates supporting my earlier figure, all seemed to be well.  (Besides which, that was the highest volume I could get out of any of the leaky Star Destroyer models! )

But, there was a reasonable doubt, so I continued to pursue it.  Further analysis and exhaustive refit and repair of another model (especially once I realized that the SketchUp plugin is a little finicky) confirmed that the old volume was too low.   But that model was not 100% perfect either, nor ws it even terribly close to such even after my hours of revisions (undertaken since the model was "easiest" to fix, without realizing its proportions were so badly off).  

Using this model and altering its proportions to match the TESB-style ISDs results in a very close match when overlaid against film images.  Thus, the volume should be reasonably accurate now.  

18a.  For reference, assuming a Star Destroyer 1609 meters long, a Star Destroyer of the Avenger type as seen in TESB should be approximately 821 meters wide and with a primary hull dagger some 202 meters tall, based purely on near-orthographic scenes from the film (e.g. the front-on view of the Falcon chase, or the bottom view during the collision scene, et cetera).

However, others claim different figures.  Such problems come from various sources, mostly related to using assorted non-canong drawings rather than the completed film.  Also, however, is the fact that there's more than one correct value.  You see, the ISD model for Episode IV and the one made for Episode V (commonly referred to as the Devastator model and the Avenger model, respectively) have differing proportions in addition to different detail work.   The smaller Devastator model, which had to be replaced ... a victim of its own success insofar as wowing the audience with hugeness and intricacy ... is commonly said to be proportionately wider.

On this page, you can see images linked to above the text "Ventral views of the Devastator".  Most everyone seems to use the first image for width, which is odd since the model is missing pieces and has odd shadows and whatnot.  Also odd is that the first image shows a model that is too wide, her width some 63.26% of her length.  This is the source of the width estimates of around 1015 meters (about 63% of 1609).  However, the second and third images (the blueprints and a model shot) seem to agree on a ship around 915 meters wide, or 56.74% as wide as long.  This is especially interesting given that the model shot shows the finished model (albeit flipped port/starboard), unlike the first image.   It seems likely, then, that the 63% value is far too much.

Even high-quality and revered fan reconstructions differ from the film ship.  The "fractalsponge" mesh of an ISD, for instance, is amazing to behold.  However, if you overlay with transparency scaled to the bridge tower from the almost-directly-front view of the ISD with the Falcon in front of it from TESB, it's clear the mesh is far too wide.  True, it's a film perspective view versus a perfect orthagonal projection, but the bridge towers being in the rear make it a reasonable comparison.  But even simply scaled to the widest points of the primary hull, the primary hull dagger is too tall.  The reason for this is that fractalsponge developed his model based on the Devastator and shots of it like the excessively-wide one from Curtis Saxton's site, adjusting details to make it resemble the Avenger but doing none of the proportion changes required.

Similarly, the scratchbuilt four-foot model here  is based on popular EU drawings that peg the ship in the 885 meter width range 55%, somewhat close to the original Devastator but still another distinct value.  Suffice it to say that for a vessel with such a generally simple shape, it is really one of the most confusing ships out there, judging from all the differing opinions.   

Also, just as a reference note, bear in mind that the Avenger dagger's top half (as measured from the middle of the ship's trenching) is of a greater height than the bottom half by about 17.986 percent . . . that is to say, the dagger shape's not symmetrical in regards to top and bottom.

19.  The Falcon volume has been altered from its earlier value, based on an unknown LightWave model.   As with the ISD, rim thickness is the main factor in estimating the volume correctly . . . a rim just a bit too thick can drive up the volume substantially.   The current value is based on this model, which fits quite well with the ship shown in this article.  The model volume was calculated based on a ship a little over 35 meters long, but given that the model is missing all the extra greeblies and whatnot this figure is probably about right.

20.   The Munificent is a curiously empty vessel.  Watching TCW carefully, you'll note that the forward dorsal hull's outline is largely composed of big pieces of metal hanging out in space doing nothing beyond being external shield walls.  Very odd ship.  But  here's a pretty model of it.   With some tweaks to get all the assorted details to read right in with the SketchUp plugin, one can get the value above . . . but that reading is based on the external shield walls having no volume whatsoever (which is good, since the aft ones are not connected to the ship at all).    As seen in TCW, the metal pieces can be knocked off with no apparent leaks or fires or anything else occuring, suggesting that they aren't even used as gastanks or anything . . . just external shield walls.

So, for mass purposes, I would bump things up a bit, since I'd imagine the ship's volume is smaller in comparison to her mass than would be the case for most Star Wars ships, which don't have goofy shield walls hanging out all over the place.

21.  The Monsterprise (the 2009 movie Enterprise) is included here only for the sake of curiosity.  It's called Constitution Class by some materials, but this is confusing with the real Trek universe.  Hence "Alternate-Reality Consitution", or Altstitution.  (Substitution Class might work as well.)   But in any case, if you take the TMP-era Enterprise and scale her up to 762 meters, the ship's volume would be about 3.66 million cubic meters, and 3.87 for the TOS Enterprise.  Per this SketchUp model, a 762 meter Monsterprise reads 2,824,395 at 5%, but that's only about half the proper value for some reason.   For now I've removed the readings and I'll try to get the correct volume when I'm done with more important vessels.

Incidentally, the Kelvin (which, contrary to some erroneous claims, is also an alternate reality ship) is supposed to be 1500 feet long, or 457 meters.  That would give it a volume of 989,000 cubic meters, per this model, which seems at least roughly accurate.  The Kelvin's size would make it about as long as the Excelsior ("My god, that's a big ship"), and with greater volume.

Also contrary to common claims, the Narada is not a ship we should expect to see in the normal Trek universe . . . the 2387 timeline from the JJ Abrams film is not presented as the same as 'our' 2387.

22.  The very pretty Munificent model I measured to within 5% gave me a volume of 2,137,120 cubic meters. A simple Venator model at the same accuracy nets me 10,616,929 cubic meters . . . a difference of almost five times, despite the ships being only 1130 vs. 830 meters (the Muni's shorter). (For reference, the Muni's volume is less than a Sovereign Class Federation starship, and she's 130 meters longer . . . we all know how sleek and spindly the Sovereigns are.)

Given that much of the Venator volume is composed of carrier-related space, though, she's really a big empty ship. If we assume half of her volume is dedicated to fighters, then the ship's only about 2.5 times the volume of the Muni, which (in concert with life support and other humanoid crew requirements) gets us closer to understanding the combat ratio from TCW.

23. The Invisible Hand is superior to the Munificent insofar as having interior space, but remains a somewhat smallish design for Star Wars.

24.  Yes, I know the AT-AT is not a ship.  But as big as it is it might as well be.   However, the mass is probably off some, since the mass of an AT-AT is constrained by the snow and ice of Hoth.  It's a question of ground pressure.  Consider that, per the model, the round part of the feet is 3.862 meters wide for a 22.5 meter AT-AT (the toes are left out).   The area of one foot is thus 11.7143 square meters, and the area of three feet (assuming one foot at a time moves) is 35.143 square meters.  A 615 ton AT-AT would thus put up to 17.50 tons per square meter on those three feet (ignoring center-of-mass issues and whatnot).   That's 171.62 kilopascals, or 24.9 psi.   

Per an unsourced Wikipedia entry, the human foot is 55kPa, a tank is 103, an SUV is 170, and a horse is also 170kPa.  A passenger car might end up at 205kPa.  Given that Luke and the AT-AT were sinking or not sinking into the snow pretty much identically, we might prefer an AT-AT somewhere closer to 55kPa.   That would limit us to somewhere below 200 tonnes.  (One could presume that antigravs were involved, but if so then there would've been no need to send walkers . . . simple fighters or speeder-type vehicles would've been much faster.)

25.  A nice X-Wing.  Also, here's a good TIE.   As always, don't forget to rescale.

26.  Here's the SketchUp of the small Republic cruiser known commonly as the Consular Class.  This is the type of ship that took Qui-Gon and Obi-Wan to Naboo in the beginning of TPM, and has been seen in TCW.   The bridge module of the model is a little bit off, but I'd consider the ship to be generally quite accurate.

The usable volume of the ship is quite a bit smaller than the value given, considering that something like a third of the ship is engine.

27.  A wonderful looking Jem'Hadar battleship model here.  The volume seems to work out well for the 1500m ship, given that it is much meatier than the big open Romulan Warbird.  Both ships are at 5% accuracy.

28.  The Vulcan Suurok Class is described as the Surak and Sh'ran classes at EAS and even DITL, but the episode script and closed-captioning call the class Suurok, and I see no need to split the classes of the two CGI models used.  The first CGI model simply wasn't as good for close-ups, so a new one was made, albeit with minor differences.  The impulse drive, most notably, goes from a TOS-shuttle style of rows to a TMP-esque dual shape . . . I prefer to think of it as the Suurok A and Suurok B classes, if one must make a distinction.  The window rows are virtually identical in any case.

The presence of a vessel almost as long as a Galaxy Class and almost exactly as voluminous as an Akira in the 2150's Vulcan fleet seemed odd when it first appeared, and still can.  Perhaps the class was the "Spruce Goose" of its age . . . possible, but unnecessary and not economical (perhaps especially without efficient Vulcans running it).

The model here can be converted for SketchUp use.

29.  The Krenim Temporal Weapon-ship is a one-off design that was erased from history, but nonetheless is such an interesting vessel that I had to add it.  The model is here.

30.  The Daedalus here is almost a perfect match with side schematics at Ex Astris.  A quick perusal of 3DS or LW ships available online suggests they are not so perfect, and thus I have replaced the older, smaller volume value.  I don't mind much either way, given the voluminous NX Class.

However, I note that primarily to point out that my 175 meter length is yet another different value.  Official stats for the Daedalus put it at 105 meters, which is too tiny.  Bernd at Ex Astris did a window analysis strongly suggesting 180 meters.  But, concerned about the ship looking bigger than the Constitution and concerned about its nacelles being proportionally too small, he dropped it to 140 as a compromise.   And DaedalusClass.com argues for a 160m ship, which is presumably a compromise-compromise.   

As for me, given the tiny nacelles of the NX Class I can't see disregarding the windows on that basis.  And given the huge-mongous-ness of ships like the Vulcan Suurok or even the Andorian Kumari Class, large ships in the 2100s don't bother me quite so badly.  In any case, at 175 meters, the ship is basically the same as the 180 meter ship (it's a 2.8% difference in length), but it shaves the volume nicely.

31.  The combined Prometheus is a good-looking ship, but it is my least favorite design simply because it's so wank-tastic given the "multi-vector" nonsense.  But that's Berman and Braga for you.  The designer, Sternbach, was following orders, and he followed them well.  That said, the tiny nacelle pair on the saucer does look especially silly, which is extra-ironic given that the saucer is the most voluminous section of the ship.   The mini-nacelles are about as large as an entire runabout, but even Voyager's tiny nacelles are enormous monsters by comparison.  I suppose we can presume that either there are extra supporting warp-sustaining doodads on the hull, or that the mini-nacelles are going nuts when active and have a very short service life (e.g. hours), or that the ship can't go to warp by itself, or perhaps all three of those or some combination of such options (or similar).  But that makes the destruction of the center section even more of a problem than it already would've been.

The SketchUp model by "Pagan" is here.  The new volume value replaces the older value of 769,670 cubic meters.   That value was probably based on the original LightWave model which was converted to 3D Studio Max format and available online (e.g. at the now-defunct Star Trek: Australia website).  Nob Akimoto probably used that one, and I managed to find a copy of it ... SketchUp will import .3ds files.   Comparing the two, I found both to be off compared to the CGI model . . . parallel renderings were shown in Star Trek: The Magazine and are available at EAS.   The Pagan model was closest, but the saucer dimensions were too large.  Thus, the volumes you see here are of my unpublished model revisions ... I had to reproportion the model saucer section.  This resulted in the upper neck connection not quite working as well (I didn't get too complex with my reproportion job), but does make a much closer match than the old .3ds model.  The surface area is of the original model ... it should still be reasonably accurate.

The length of 414.5 comes from Rick Sternbach (1360ft.), corresponding closely to the EAS length.  Lengths for each section are simply measured from the revised Pagan model.

The vessel when combined is almost certainly quite a bit heavier than vessels of comparable size, given the extra hull mass and additional replication of parts.

32.  The New Orleans volume is a little low.   The model available online has a shortened engineering hull which connects further back on the saucer and does not extend back quite as far.

33.  There's a Cardassian Galor model here with bad volume, but comparing with the CGI available at the Drex Files, the model proportions are off . . . the main hull is squished down pretty well, which probably contributes strongly to the tiny deflector/weapon emplacement that is a short rectangle on the model, but should be a square.

34.  A lovely Delta Flyer, Runabout, and Type-9 shuttle combo pack is here.   

You can find a less accurate Runabout here, and from what I can tell that's a SketchUp import of the 3D Studio model (also available in LightWave)  found elsewhere online.  However, that model has proportions that do not match the DS9 Tech Manual top and side views available on EAS, and aren't the same as what we would expect from the show.  The nacelles are skinnier and riding higher than the bottom of the fuselage, for instance, along with other inaccuracies.  (Of course, that model was probably made before the DS9TM or any other schematic views came out, so it's quite forgivable. That said, the DS9TM views are also wrong, but close.  The nacelles are kicked back a couple of feet in the 4-view compared to the model itself.)

As such, I have replaced the old 542m³ value with the better SketchUp Danube's volume.

35.  The Nova Class is often scaled at around 150 meters based on a computer screen comparison of the ships in "Equinox, Pt. I"[VOY5].  However, the computer screen (often identified as an MSD comparison) was actually in 3-D form, and folks seldom seem to recognize the offset between the two vessels on that screen (the Equinox was a bit behind Voyager).   A more careful look (which corresponds nicely with the exterior view) shows that the Equinox was a little longer than is commonly thought, being long enough that if the sterns are both at zero, her nose extended almost all the way to the forwardmost bottom of Voyager's engineering hull (under the deflector dish).   That's more like 180 meters, give or take, which happens to correspond nicely to Bernd's EAS estimate of the ship's length based on window rows.

The A-type and B-type Novae are scaled to the same points on the hull and are based on a 180 meter A-type.  The B-type's extra nose resulted in a total length a hair under six meters longer.   Given the smaller saucer deflector on the B-type, I actually rather doubt that the mass is signficantly greater than the A-type, if at all.   Her density should be close to Voyager's given that the Nova A-type was intended for planetary research, and both types seem to have landing leg doors.  Note that the B-type Nova's surface area is a guesstimate based on the A-type.

The SketchUp models by Pagan of the Equinox and Rhode Island have replaced the earlier model, which appeared to be excellent but perhaps a little pudgy in places.

36.  The Romulan Bird of Prey of the 2150's has potential scaling confusion.  The TOS BoP of a century later is often assumed to be in the 130m range, but opinions vary widely on the ENT BoP.   Scaling from the two rows of saucer-edge windows gives 260 meters assuming 3m decks (as DITL does), making it longer than Enterprise.   On the other hand, the same concept applied to the windows near the saucer top results in an even worse hugeness in the 430 meter range, since those windows are closer together.  On the other hand, if we assume the saucer thickness must represent at least two decks, then giving 6 meters for that entire height (thus assuming a somewhat non-standardized window placement) gives us 163 meters.  Coincidentally, this is very close to the 165m from a backstage scaling diagram Rob Bonchune once posted, though he implied that they would alter scales to make the shots look 'better'.   The two window rows near the saucer top still don't enjoy that value, though, and we would have to assume some funny business for the windows in that area.

However, the corridor heights seen on the Romulan vessel from "Babel One"[ENT4] are pretty tiny . . . probably not much more than 7 feet, if that. Giving some wiggle room and making it 7.5 feet (2.286m), scaling the saucer-edge window rows from that gives us 198.6 meters for the length of the ship. 200 meters it is, then. 

The model used is from an excellent Bridge Commander mod.

37.  The Klingon Bird of Prey of the 2150's is also a scaling pain.  One of the better occasions for scaling to occur was the Augment arc.  Yet "Borderland"[ENT4] suggests a BoP around half the length of Enterprise (~115m), though given the much thinner neck section this would start to cause structural and transit problems.  In "Cold Station 12"[ENT4] we get to see a Denobulan vessel interior and exterior along with entry into the Bird of Prey's shuttlebay (a shuttlebay!) . . . and the ship seems it must be 200 meters long.

Given the presence and plot requirement of a shuttlebay, and the fact that even a short one as shown requires a ship of a decent size, my temptation is to split the difference, which would be about 160 meters, very close to three quarters the length of Enterprise at 169 meters (and satisfying the old TNG-era "alien ship is 3/4s the length of the Enterprise" quasi-rule).  So, right around those figures gives us 165 meters.   That's enough for the neck structure to have four and a half meters or so to work with for corridor and such, and gives a 5 meter tall shuttlebay door (give or take).

The rather less clumsy and more slender-looking Bird of Prey from the 23rd and 24th Centuries would, if 165 meters long, give a volume of 136,300 cubic meters.  

38.  I thought the funny ringship USS Enterprise had no readily discernible length.  I therefore simply scaled it based on the rough minimum requirement for a guy to be able to float or travel crouched down the central neck tube, and even the tube itself was no real guide given that (a) this was just the tube diameter some guy picked when making a model of the ship, and (b) there's no reason to assume anyone could inhabit the tube anyway.  Images from the paintings of the vessel seemed to show a more slender neck tube in any case, which would drive up the length (but not the volume).

But as it happens, there are actual blueprints of the ship.  On the Drex Files blog, commenter Vahmp shared some wonderful blueprints by Matt Jefferies for the ringship, which had originally been part of an unused television concept.  The ship in the blueprints scales out to about 395 feet, or 120 meters.  However, I will wait to update the information given on the site pending further work with the model itself.  Thanks Vahmp!

The vessel mass provided above is nothing more than a wild guess, even beyond the length issue.   The ship was certainly built before 2143 and presumably built after 2063, in which case it should be made of more modern-day materials and hence ought to be quite a bit lighter.  But that depends in part on her origins.  For instance, the ship could be a human vessel built around some old Vulcan or other found warp coils, which would put it existing anytime in that 80 year span.   Or it could be a human attempt to copy Vulcan warp methodology, leading us down the garden path for awhile until we finally figured out that Cochrane's way was the way to go (which would explain why it took 80 years to pass warp two with nacelle-based warp drive).   Or it could even be a completely separate government-sponsored warp drive experiment, much like Samuel Langley's government-sponsored flight attempts that failed while the Wright Brothers succeeded.  That might suggest a very light ship for its size.   Or some combination of these.

Or it may have nothing to do with warp drive at all, and instead may be some experiment on (or vessel using an early version of) subspace-driver-coil-driven drive products (or even some 'lower tech' magnetic ion-drive-related technology), as suggested by the big honking pillar of fire coming out the backside in most images.   It may simply be a pre-warp vessel from the completely different timeline that had featured the Nomad probe and Eugenics Wars and other such things.  

In short, we'll never know, and the sky's the limit.

39.  The freighter listed here is the rather standard Norkova / Xhosa type.  I would wager that this is the  Type 2 Freighter compared to the Type 1 of the Batris configuration, whoever the manufacturer may be.   In any case, the model (obtained from a Klingon Academy mod) required extensive modification to make it work for volume calculation, and one large piece of equipment (the round thing on the upper portside structure) is missing from the final model as measured.  Nonetheless, the value above accurately relates to the main hull's configuration.

Given that this is a freighter, chances are good the mass values are too heavy for the ship itself (I imagine it's built light), but may be accurate with the inclusion of cargo.

40.  The Aerowing or aeroshuttle is the Intrepid Class Captain's Yacht, never seen or hinted at in Voyager (implying Voyager's wasn't there).   It's the obvious runabout-esque ship shape on the underside of the Intrepid saucer.  The model used is based on renders that never made it to the screen.  While not strictly canon in its entirety, we've seen the bottom of it and the top is plausible enough, though from a real-world view it would still make more sense if they'd simply hard-docked a Danube there and thus spared themselves the expense of another ship design.  So, take this one with the appropriate grain of salt.

41.  The Romulan Scout is one of my favorite Romulan ship designs.  The model is very basic, but with some modification it worked fine.  I find it odd, though, that a ship so large (larger than an Antares and almost half the volume of the Defiant) is so often seen with just one person aboard.   Then again, in the early TNG era small crew counts were the norm, what with all those low-crew Mirandas running about.

42.  Here is the model for the Scimitar.

43.  Previous versions of this page featured a 50% mass reduction for the mushroom type starbases.  However, I'm leaving the full values there at present, but if it were me I'd halve them at least before use.  For instance, Spacedock is probably an expensive starbase, but I rather doubt it's worth 26,000 Constitution Class starships by volume.  Then again, even if it's only worth a third of that, it's still 8500 ships, which is not terribly far from the number of ships in the Starfleet of the 24th Century.

44.  Commonly known as the Romulan shuttle but which is sufficiently large to be runabout size, the mesh available here took forever to fix up enough for the volume plugin to work upon it correctly.  That said, despite being a very simple model in basic shape, the representation is quite good.

45.  The Sydney volume is based on an Armada mesh.

46.  I approve of the Twilight in principle, but it's just about the only Star Wars vessel with the primary thrust being unquestionably way off the centerline.  That's a shame . . . only Trek was doing silly stuff like that before (though even then not quite to the Twilight's extent!).

47.  I rather like the Republic Light Cruiser, even though some of its Star Destroyer-inspired design features (like the hints of superstructure around the bridge tower, not to mention the bridge tower itself) are kind of silly for a ship that small.  It basically looks like a Falcon front end got mated to a Consular rear end with Star Destroyer pieces in the middle, but it still works somehow.  I just hope we get a better name for it at some point.   It was identified by Separatists as a vessel of an escort class, but they lumped it in with three smaller Consulars to make that statement.  The vessel length is a rough estimate on my part.  It could easily be 150 meters if the structure of the model I used is any guide, but it looked a little bit bigger to me in comparison with the Consulars trailing it.

48.  The Tantive IV, "galactic cruiser" and "blockade runner" per the ANH novelization and script, respectively, has a remarkably large volume when compared to the slightly longer, much wider Republic Light Cruiser above.  I was worried for a moment after adding the Republic Light Cruiser that something was wrong, until I remembered just how absurdly huge the engine cluster is on the Tantive type.  Then I relaxed.

49.  The Kumari was the topic of this blog post on the difficulties of getting some of these models to perform well when under volumetric scrutiny.  After having already expended enormous time cleaning out the innards ofa "fat-bottom" Kumari with a very large aft section and a taller head, I finally bit the bullet and fought against the innards of the best looking mesh I could find (when compared to Doug Drexler's orthographic views), and that's the result.  

50.  The excellent Type-7 here shocked me at first with its large size compared to other shuttles, but it is accurate.  Unexpected that it's 9 times the volume of a shuttlepod, though.

51.  The Type-15 model is very good.  Estimating the volume for this one by eyeball proved quite a ways off, too . . . I didn't think it would go above 7. 

52.  Took awhile to get a working Raven model . . . the one obtained from the now-defunct Star Trek: Australia site and credited to SciFi-Art does not perfectly correspond to the EAS depiction, but it is adequate.

53. The NX shuttlepod I found required extensive reworking. Starting with the structure of this low-poly Bridge Commander model that was basically a hexagonal bullet, altering the proportions and heavily reworking the nose, windshield, and upper rear (the model as built relied heavily on texturing to 'cheat' the appearance of correct structure), I tried to make the vessel correspond fairly well to Raul Quiles' five-view here and to my own eyeball appraisal, and I somehow found a length of about 8 meters initially.  But, thanks as always to Flare, where an official length of 6.9 meters was noted as having come from the 2010 Haynes tech manual.  After further review and additional comparison with the Doug Drexler renders of the actual CGI model as shared by Bernd, the suggested height for a 6.9m shuttlepod appears to better correspond with the practical set compared to the actors and their known heights.

54.  The Kazon Predator / Kazon Carrier / Kazon Mothership (the name depends on who you ask) is a big enormous beast, and has been due for inclusion on this page since 2003 when it was first requested (the request was fulfilled in just under seven years).   The model used is imprecise compared to the EAS depiction (the upper hull is too short, the lower face too deep), and would require extensive rebuilding to match perfectly.  However, it is generally accurate and most of the problem areas either cancel out or leave the size a little low, which I'm okay with for the time being.

55.  TOS Romulan Bird of Prey information per my rationale in this thread and a cleaned out version of this model (rather difficult given the modeled bird going all the way through the ship, but eventually do-able).  I used to have the Romulan Bird of Prey from TOS in the 131 meter ballpark, but I just don't think that's so anymore, as noted in the thread linked.

Interestingly, this implies that the habit of Romulans to have larger ships than what the Federation was sending to greet them started as early as TOS, given that the 192 meter Bird of Prey is twice the volume of the Constitution Class.  Given the cat and mouse of "Balance of Terror", it's amusing to ponder that it was a rather big mouse.

56.  Considering that the Y-Wing is bigger than an X-Wing even without the Clone Wars-era extra fairings and whatnot, yet is evidently a functional fighter, one wonders what's missing.

57.  Deep Space Station K-7 . . . pretty nice little model, here.  It's a fairly simple design, a triradial design like DS9, but it looks tiny and a little silly by comparison.   One thing I still don't get is how (or if) you can actually dock with the thing.

58.  I can't believe I forgot to add the Borg until mid-2010.  

In any case, the cube gets a perfect score on volume coefficient (surprise, surprise), and the sphere gets the perfect score on volume by surface area (surprise, surprise).   As with the Death Stars, though, both of those values are simple calculation from the basic shape, not a true figure.  The outer surface of the sphere, for instance, is so gnarly with greebles that the true figure would be less. 

The sphere's estimated diameter comes from "Regeneration"[ENT2], when a human scientist estimates the size of a crashed sphere based on the curvature of the outer hull debris.

The volume of the cube is taken from the direct statement in "Dark Frontier"[VOY5], and the length of the vessel is calculated from that.  Assuming 28 cubic kilometers was a round up or round down, the true volume would likely be anywhere from around 27.5 to 28.49, with the length thus working out to a range of about 3,018 to 3,054 meters.

Interestingly, given its size the tactical performance of the Borg Cube is not terribly impressive.  By volume, the cube is worth 4800 Galaxy Class ships, and 32,000 Excelsiors.  Even by surface area alone, the cubes equal a thousand Galaxies at least.   And yet in First Contact, Starfleet (with only a little targeting help) was able to destroy a cube, and so far as we know they didn't experience even Wolf 359-level losses, which by volumetric measure were exceptionally light.   

Presumably this explains the origin of the tactical cube, which might be nothing more than an uparmored cube that's designed to keep better pace in regards to a firepower-to-volume ratio . . . or so we might say, but for the fact that Voyager tangled with one twice for minutes at a time and lived to tell the tale.  Some theorize that the tactical cube was damaged or otherwise in poor condition, which makes more sense.

One impressive thing is the Borg Sphere being knocked out by four quantum torpedoes in First Contact . . . despite being worth 129 Excelsiors (or almost 47 Sovereigns), the quantums took out huge (~50m) chunks of the sphere before the entire ship exploded.

B.  Tips and Tricks for the DIY Volume Calculation Guy

1.  SketchUp

1.  There is an update to the Volume Calculation plugin for SketchUp, but you don't want a version beyond 1.8 because the code was changed in 2.0 . . . this made it faster, but less able to deal with complex shapes (like starships).

2.  After running, the plugin asks if you want to hide the ship.  You do, because then it will show you the volume section planes, which should be evenly spaced and thus allow you to make sure of what it has actually calculated.  Many ships, for instance, will seem to have a volume reported that is too low, or in the case of DS9 too high.  Checking the section planes can allow you to see if the plugin missed a section of ship (as often occurs with a poorly-built model mesh) or is adding something extra.

If you're feeling especially frisky and the volume can be calculated quickly, you can turn up the accuracy to see exactly where the leak or other problem is occurring.   Also, turning a starship around on its axes can be helpful when trying to get the volume plugin to calculate a ship correctly, or to find the leak.  Last but not least, running the volume plugin and then running it again with the ship (and grouped volume section planes) at a different orientation can be a good fix of last resort when you just can't get a ship to stop leaking.

3.  As with most model volume measurement tools, the interior of the mesh should, ideally, be free of junk.   Of course, as hinted at above, you'll find that almost nobody doing sci-fi mesh work bothers to clean out the interior of the ship mesh when it's done, so you may find yourself learning how to delete things.   

In SketchUp, selecting the whole ship in non-group form and intersecting all of its parts will allow you to start cleaning out the interior.  You'll also want to make sure that no faces are reversed (i.e. outer surfaces pointed inward), though this may not be as critical depending on different factors . . . I've been doing it anyway, though.  It can be helpful when trying to do that to change the style settings so that face sides strongly contrast one another (but not to the point where the color hurts your eyes after extended viewing).  Bright interior color can also help, though, for looking around a model to see if there are any gaps.  If so, you may find yourself having to connect the dots or, in the case of a very poor model, doing a little refit and repair work.

2.  Blender

1.  Instructions on how to calculate volumes using a Python script for Blender can be found here.

Special thanks to scifi3d.theforce.net, the Lightwave Group, TrekMeshes.ch,  KlingonAcademy.com, Foundation 3D, and to all the modelers who have spent so much time making their vessels.  Special thanks to modeler Joe McMullen who contributed an early value for the Nova based on his exquisite mesh.  Special thanks to "Axeman" for contributing data on his excellent Type-7.

Extra special thanks to Flare poster "blssdwlf", who pointed out the existence of the "gross ton" mass measurement.