What word describes the amount an object is filled to, regarding its capacity?

Given an object that can hold a capacity of something, is there a word which describes the current amount it holds towards that capacity?

For example, if an elevator has a capacity of 20 persons, and the current number of occupants is six, the elevator's <some property of the elevator> is six?

Update: The commentary on @jwpat7's excellent answer made me realize something which hadn't occurred to me: the nature of the container and the things it holds have an impact on the appropriate description. I picked an arbitrary example using people, but the reason I've been seeking this word is to describe discrete (i.e. not something like liquid in a tank) inanimate contents.

A better example would be: an egg carton has a capacity of 12 eggs. It currently holds 7. How does one describe the amount currently held: "The carton's <this> is 7 eggs"?

Occupancy seems like the natural word for what you ask, per oxforddictionaries:

the proportion of accommodations occupied or in use

(Edit: The most applicable sense of it in wiktionary is

The act of occupying, the state of being occupied or the state of being an occupant or tenant

which is rather less satisfactory than the definition shown first.)

Here are some other possibilities: population, headcount, crowd size, census, number, complement, company, fraction. A rarely used term is filledness. Of all these, headcount perhaps fits best into your example, but others fit with minor rewording:

The elevator's headcount is six at the moment.
Those in the elevator number six at the moment.
Those in the elevator are six in number.
The elevator party is six in number.
There are six persons in the elevator.

Comment: As the last of those examples illustrates, one doesn't need a special word (besides in) and you may need to revise your question if that being so is unacceptable for some reason.

I can't think of a word that would fit in, "The carton's X is 7 eggs." I think the conventional way to say this would be, "The carton contains 7 eggs" or "The carton has 7 eggs in it". If it's something that normally starts out full and is used up -- like an egg carton -- you might say "The carton has 7 eggs remaining" or "... 7 eggs left."

If you're thinking in percentages, it's common to say "The bottle is 35% full" or "The box is half full."

You could, of course, dig out some obscure word or invent a word, but as tchrist notes, it's usually better to use ordinary language even if it is somewhat less concise. I avoid using obscure words or attaching specialized meaning to a word unless I need to use it a lot so it's worth the effort of explaining it.

For inanimate objects, I would suggest contents; the carton's current contents is 4 eggs (out of 6)