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.
-
Yeah I think bungie just -blam!-ed up scaling wise in the picture and like you said only did it to make it look badass.