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When we talk about height, usually we mean the distance from an object to an external zero reference such as the ground. I'm looking for a single word that describes how much height is resting on or hanging from an object, where the object itself is the zero reference. For example:

If the top floor has a ____ of zero, then the third floor of a five-story building has a ____ of two.

If there's a word for this concept in mathematics, that would be ideal. Or a word from genealogy expressing the number of generations of descendants a person has. A word from architecture or shipbuilding might also fit. I considered the word freeboard, which is roughly the height of a ship above the waterline, but the reference always seems to be the waterline. I don't think you'd speak of the freeboard above a particular deck. I also thought about the word load, but I don't want to express the total mass or volume of stuff, only the dimension of height.

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  • I don't believe there is such a word, except perhaps as architects' jargon or some such.
    – Hot Licks
    Nov 26 '15 at 19:12
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Depth.

I think. At least, that's the word that I would complete the sentence with. However, I don't know of a word that is a really good fit.

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Load.

That's the word that is the most obvious here, but from your description I'm only 99% sure. :D

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  • Sorry, I just edited the question as you were posting this answer.
    – Kevin Krumwiede
    Nov 26 '15 at 18:18
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    Ah, yes, now... well, I'll still leave it here because I don't want to anger the dwarf in me. :D
    – Jürgen A. Erhard
    Nov 26 '15 at 18:25
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elevation may fit.

It is the height to which something is elevated or to which it rises (It refers sometimes to the altitude of a place above sea level or ground level).

Example: The elevation of the tower is 80 feet.

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'Descent' works. It's a somewhat unusual use, but legitimate and understandable:

descent, n.
5. any passing from higher to lower in degree or state; decline.

(descent. Dictionary.com. Dictionary.com Unabridged. Random House, Inc. http://dictionary.reference.com/browse/descent (accessed: November 26, 2015)

This works with "height" in your example sentence; it would also work in a similar genealogical context.

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  • The problem with descent is that it's a travelling word -- an action -- whereas the question required a static word. That is, the floors aren't moving!
    – rivimey
    Nov 28 '15 at 17:21
  • @rivimey, Well, I upvoted your answer, because I think it works also and I might have used 'depth' in addition to 'descent' if you hadn't gotten there first. However, no offense, there are concrete, abstract, and figurative senses of 'descent' that aren't "travelling" words: consider mountain climbing, where 'descent' refers not only to the action of descending (one sense of 'a descent') but also the route down (another sense). This is especially noticable in genealogy, where it can refer to a generation.
    – JEL
    Nov 28 '15 at 22:41
  • JEL, thanks for the upvote, and no offense taken :)
    – rivimey
    Nov 29 '15 at 3:08

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