We know that the Imperial Fleet is insufficient to keep the "million systems" of the Empire in line. This suggests  that the Empire does not have more than a million or so heavy ships, but makes very little clear.

Han Solo notes that it would take a "thousand ships" making use of "more firepower than ever existed" to demolish Alderaan, and then notes that the Imperial Fleet couldn't possibly accomplish such a feat. This on the one hand suggests that the Imperial Fleet contains less than a thousand ships - at least, could never assemble a thousand of its strongest capital ships together - and then also suggests that the capabilities of the Death Star is one that could not be replaced by a conventional fleet that the Imperial Navy could assemble at this point in time.

The Death Star is also suggested to have firepower in the neighborhood of half the Imperial Fleet. Some say (see right) that this must refer to the surface firepower of the Death Star.