Once a week, I ask my first-year law students a language puzzle, often focused on legalese but sometimes on broader English usage matters that can arise in legal work. Yesterday's puzzle involved the distinctions between permissive and permissible, between conclusory and conclusive, and between enormity and enormousness. I noticed that none of the student volunteers could answer the enormity question — and when I discussed it later with some other very smart and well-educated people, I saw that they were unaware of the (possible) distinction. I therefore thought it was worth blogging, for the benefit of our similarly very smart and well-educated readers.
Here's the distinction: While enormousness generally means "very great or abnormal size, bulk, degree, etc.; immensity; hugeness," enormity is often used to mean "outrageous or heinous character; atrociousness" and "something outrageous or heinous, as an offense." Therefore (a) "enormity" makes some listeners think of something bad, and (b) some people believe that the use of "enormity" to mean "enormousness" is an error.
As it happens — and I stressed this to my students — "enormity" has long been used to mean "enormousness." The OED attests this back to 1792, and Random House reports that "Enormity has been in frequent and continuous use in the sense “immensity” since the 18th century." I therefore wouldn't say that the use is thus "incorrect" in any objective sense.
Nonetheless, both the OED and the Random House report that the use is regarded as incorrect by at least a considerable number of people; my law students, I think, ought to know this, so that they don't inadvertently alienate those readers. (If they knowingly alienate them, because they refuse to be bullied by the Language Police, that's a different matter.) Moreover, even readers who aren't so picky but who associate "enormity" with something bad might be distracted by the term: If you say "The enormity of his generosity impressed me," you'll at least be distracting readers, even if they understand what you mean and don't deliberately hold your word choice against you. If you write about "the enormity of the task," you might lead readers to wonder -- even if only briefly -- which meaning you have in mind. So I would caution people to avoid using "enormity" to simply mean "large size," though as I said I don't think I can objectively call this a language error.
UPDATE: I should have mentioned two other things. First, I'd probably caution people away from using "enormity" even in the sense of "atrociousness," unless the context is such that even those who read "enormity" as being "immensity" will get your message. "Enormity of his sins" might be fine; "enormity of the task" probably will be confusing. It may be too bad that many intelligent, well-educated readers don't know the word, but that seems to be the reality.
Second, "enormousness" strikes me as pretty clunky; I'd suggest "vastness" or "immensity" or some such instead. I'm not recommending its use -- I'm just cautioning against using "enormity" as a rough synonym for those three words.