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.