As long as you have a managed library, the best thing to do is to quit Aperture, and from the Finder, look for your Aperture library, then click on the icon for the Aperture library, and go to the "File -> Get Info" menu option.
It may take a few minutes for the Finder to figure out how large the Aperture library is, depending on its size, but that should give you a good outside estimate of how large your vault is going to be.
If it was originally an Aperture library, hit Command-Space to open up Spotlight, then type in .aplibrary. That should bring up a list of all the Aperture libraries on your computer.
Click on "Show All in Finder" to bring up a Finder window with the search results. From there, you can click on your library and perform the "Get Info" command.