It's pretty easy to do. You can see how big it is in relation to Saturn's rings during the arrival cinematic for the new Crucible map, The Dungeons.
Saturn's rings are 73,000 km wide. From the cinematic, the Dreadnaught is about 0.07 times as long, and in the same plane as the rings. That makes the Dreadnaught...
[b]5110km long![/b]
That's over 5 million metres.
From other, better quality images of the Dreadnaught, I've calculated that one side of one of its square ends is about 0.3 times as long as it's length. Therefore, that gives a total volume of...
[b]1.2 x 10^10 (12000000000) cubic kilometres![/b]
So, yeah. It's pretty damn big.
[b]Edit:[/b]
Obviously, I am not expecting that we will be able to visit even a tiny fraction of this. Just like how we cannot visit all of the Earth, Venus, etc.
Also, I find it likely that Bungie does not actually intend for it to be this big, and instead either didn't realise (or expected other people not to realise) just how big Saturn's rings are. That, or it's just to make it look more badass.
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It definitely isn't supposed to be that big. If you look at the cinematics that have been released, you can see Hive Tomb Ships next to the Dreadnaught. We know approximately how large those are so we can gauge distance and thus size of the Dreadnaught. I don't want to crank numbers but it's definitely not as large as the image in the rings makes it out to be.