"How big is the universe?"
Translation:Kiel granda estas la universo?
Kiom accompanies nouns or verbs, not adjectives. You cannot quantify a quality. Instead, you grade it with kiel.
Thanks to a comment of SquirlRat I have noticed that my comment was too categorical. According to PMEG (look under “Kiom kaj tiom pri emfaza grado”) there exist some instances of use of kiom to strongly emphasize degree instead of amount. It also says, though, that in order not to wear out this feature of the language it should be used sparingly.
From reading the sections of PMEG mentioned previously, I think
Kiel granda estas la universo?
Kiom granda estas la universo?
would differ by the sort of answer they’re expecting—the Kiel… one might be answered, “Pli grandega ol vi iam povus eble imagi!”, but the Kiom… one would probably be expecting something more like, “Proksimume 93 milionoj da lumjaroj en diametro.” You could answer either one with either answer, but these pairings seem more likely than the alternates.
Does that seem at all correct?