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When working in a 2D coordinate system you could say that X is the horizontal axis and Y is the vertical axis.

Extending this to 3D, is there a similar word for the Z axis?

(I'm aware of Width, Height and Depth, but obviously horizontal and vertical aren't synonymous to width and height, which is why I don't want to call the Z axis the depth axis.)

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Z is also horizontal in this analogy. – Hugo Jan 31 '12 at 9:58
Hmm, thinking about it that does make sense since both axis would be on the horizontal plane. Is there an alternative I could use to differentiate between the two, or am I stuck with depth? – George Duckett Jan 31 '12 at 10:00
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According to Wikipedia the three axes are called the abscissa, ordinate and applicate, referring to x, y and z respectively. So although applicate doesn't translate directly to the word you're looking for, this would be an appropriate notation to distinguish your axes. – Andy F Jan 31 '12 at 10:04
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@Urbycoz: I probably could generally, but I might end up talking about a horizontal difference between 2 objects and their widths for example. So I'd be using depth to mean 2 different things in a similar context. This is in the context of programming, where I'm after appropriate variable names. – George Duckett Jan 31 '12 at 10:04
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Whatever symbols we may use, two of the axes are always in one plane. If x and y are horizontal, z is vertical; if x and z are horizontal, y is vertical. The words horizontal and vertical are generally used in a planar (2-dimensional) sense, not spatial (3-dimensional). Which is the reason you may not find a word corresponding to the third dimension along with horizontal and vertical. Don't forget there is the fourth dimension: time. :) – Kris Jan 31 '12 at 10:18
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7 Answers

up vote 13 down vote accepted

I doubt there is such a co-hyponym (if we can call it like that) to horizontal and vertical. You'll need to use an alternative name.

If you imagine the 3 axes, then the Z would appear "on the same level" as the X one. Depending on which ones you consider, 2 of the 3 will appear as such and actually, they are.

                                                  XYZ Cartesian Coordinate System Image

If you look at the Wikipedia page for Cartesian Coordinate System, under the section Cartesian Space it says:

For 3D diagrams, the names "abscissa" and "ordinate" are rarely used for x and y, respectively. When they are, the z-coordinate is sometimes called the applicate.

Emphasis mine. It says they are rarely used, but I doubt there are many other alternative terms, other than Z-axis, depth, and so on; they're the most appropriate terms, if you're looking for something technical.

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Re: "co-hyponym": I don't know if there's a standard term for such things, but WordNet calls them "coordinate terms" (see wordnet.princeton.edu/wordnet/man/wngloss.7WN.html#sect4), which in this context is rather fitting. :-) – ruakh Jan 31 '12 at 15:08
@ruakh I wrote that part to make it clear that maybe the term wasn't the best choice, but it was the best I could think of to explain it :D – Alenanno Jan 31 '12 at 15:18
up vote 15 down vote

In aviation we use the terms longitudinal, lateral and normal (or vertical) for the three axes. See this description.

Note that these are fixed relative to the aircraft, not the earth.

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normal = perpendicular (to the horizontal, i.e., both longitudinal as well as lateral). These are with reference to the earth? Earth horizontal is really a curved plane. – Kris Jan 31 '12 at 14:10
With reference to the other two axes. It's still perpendicular to the other axes when the aircraft is in a steep banked turn (flying nearly on its side relative to the earth). – Graham Borland Jan 31 '12 at 14:17
up vote 4 down vote

Plain English words may not always suit specific technical usage.

As for variable names, you will have to drop the h-v concept and adopt the xyz nomenclature. Just remember in 3-D, the z-axis is the equivalent of the conventional 'vertical' (the entire 2-D x - y plane being the 'horizontal').

[see also my comment @OP]

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Conventions for which axis is "vertical" vary across different domains and even within domains: sometimes it's z, sometimes it's y. The direction of the vertical axis also varies: sometimes the "up" direction is positive along the vertical axis, sometimes it's negative. – John Bartholomew Jan 31 '12 at 13:30
@JohnBartholomew In fact, a three dimensional object in space has no defined vertical or horizontal. Take a cube and turn it slowly along one of its axes: what happens to the original horizontal/ vertical plane? The plane rotates with the object. At what point does the 'horizontal plane' cease to be so and become the 'vertical plane'? :) – Kris Jan 31 '12 at 14:07
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The "horizontal" and "vertical" of a coordinate system are defined by use, though I agree there are some domains in which no such meaning can be applied. My point is that saying "the z-axis is the equivalent of the conventional 'vertical'" is inaccurate in general (though it's true in some cases). – John Bartholomew Jan 31 '12 at 14:13
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In my 3D coding experiences, we have called it the z-axis and depth. As well as z-values and depth-values used to mean the same thing. And also we rarely used horizontal and vertical, we just called those x-axis and y-axis.

Both of these answers are somewhat rejected by your question, but this is the answer I give based on my experiences. Maybe if you described the context of your usage, it would help.

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right, we have to be specific, he is saying in a comment "This is in the context of programming" – Theta30 Jan 31 '12 at 20:24
up vote 1 down vote

The axis, perpendicular the the plane of the graph is usually called the normal axis.

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enter link description here

http://thinkmath.edc.org/index.php/Length,_width,_height,_depth

In describing the box or cube you would use height, length, breadth, width and depth. With breadth, width and depth being interchangeable.

I would use a diagram to or key to specify what you mean in your particular case.

x = Breadth
y = height
z = depth

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up vote 0 down vote

Original

Perhaps it's time to coin a new term? Here are a few possibilities I came up with:

  • Applicatal (derived from applicate)
  • Depthical (derived from depth)
  • Zedical (derived from Z)
  • Fordinal (derived from forward)

Edit

Upon further research, it appears that in the realm of print media, they refer to the 3rd axis of linearity as "stacked". So you have horizontal, vertical, and stacked printing layouts. Here is a link to the best explanation I could find:

In hind sight, when making user interface layouts where the items move along the Z-axis (in a list), I have referred to them as being stacked. Given that this is in the context of programming, stacked may work for you if you're referencing the linearity of a layout.

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Or maybe farcical (derived from far away) ;) jk – George Duckett Feb 3 '12 at 17:30

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