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
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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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    @Random832 I think OP already has N-S, W-E. (The compass is flat.) What next -- Zenith? – Kris Feb 1 '12 at 10:40

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

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.

  • 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
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    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


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)


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.

  • Or maybe farcical (derived from far away) ;) jk – George Duckett Feb 3 '12 at 17:30
  • stack(ed) and layer(ed) are terms that are applicable in 2.5D systems, not in true 3D spaces. – Crissov Apr 26 at 12:50

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


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

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.

  • 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

Think Math graphic

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 or key to specify what you mean in your particular case.

  • x = breadth
  • y = height
  • z = depth

Assuming cartesian, affine, orthogonal coordinate systems wherein axes are perpendicular towards each other and usually parallel to the viewport edges, the planar 2D coordinate system (for specifying positions, linear paths and areal shapes) of

  1. horizontal X-axis (abscissa) for designating left and right positions constituting distances like widths, breadths or (without a negative direction) lengths and
  2. vertical Y-axis (ordinate) for designating top, up or upper and bottom, down or lower positions constituting altitudes like (positive) heights and elevations or (negative) depths

becomes usually

  1. either the plan, ground, base or floor, i.e. what appears flat in top-view,
  2. or the canvas, face or facade, i.e. what is flat in front-view and
  3. rarely the side, wall or fence

of a spatial 3D coordinate system (for also specifying volumetric bodies). The positive directions conventionally follow the right hand rule with the thumb pointing towards X+, the index finger towards Y+ and the middle finger towards Z+.

Bottom-Up Z-Axis

1st Case

In the 1st case, especially used with maps, the Z-axis becomes the vertical dimension, which is often positive only, and either the X-axis or the XY-plane is considered horizontal. In the former case, the Y-axis has no conventional designation matching the horizontalvertical pair, and it is only ever used when both of these axis are oriented the same as the drawing canvas, which explains somewhat why there is no third term. In the latter case, no designation is necessary.

Front-Back or Back-Front Z-Axis

2nd Case

Only in the 2nd case, there are formal alternative names available: the third axis is called an applicate in environments where the others are known as abscissa and ordinate. This means, an applicate always follows the virtual line of sight of a spectator ranging – according to the right hand rule – either from negative back to positive front, e.g. in most paper diagrams with the origin in the lower left, Y+ pointing up and X+ pointing right, or from negative (or zero) proximity to positive distance, e.g. on screens and all other planar media inherently organized in horizontal lines or rows and vertical columns running from top to bottom. One could derive neologisms from these terms, e.g. *abscissalordinal*applical or *applicational.

Layout systems often use the 2nd convention, but only support a 2.5D space with multiple planes in distinct, indexed and possibly named layers that are stacked above one another in a canonical order with a thickness of zero. The equivalent to horizontal-vertical position for the pseudo-dimensional axis would be level with the derived neologism *levial.

Left-Right Z-Axis

3rd Case

Relative Axes

It often makes sense to establish a relative, local coordinate system for any (moving) object in 3D space. Its trajectory (from–towards) or (if stale) bearing of its assumed line of sight, e.g. along a nose, determines the longitudinal axis. Its lateral axis is perpendicular to this, e.g. alongside wings, and together they span a plane that is often (approximately) parallel to the ground and which the third, normal axis is perpendicular to. This triple longitudinallateralnormal basically matches <wanted term> ∶ horizontalvertical, thus longitudinal could be argued for as a reasonable candidate for the third axis in absolute, global coordinate systems as well.


Looking at a related language, there are native terms for horizontal and vertical in German: waagerecht and senkrecht, respectively. They either originate in or at least align with the desired states of beam balance scales (Balkenwaage) and plummets (Senkblei, Senklot). Accordingly, Ænglish cognates would perhaps be *scaleright and *plumbright. There is no term for the third axis or orientation in German either, but analogous construction could yield something like *eyeright, *sightright, *shotright, *wayright or *pathright.

Since X-Y-Z axes are frequently colored red, green and blue, respectively (cf. RGB color space) in 3D applications, and vert means green in French as well as in English heraldic tinctures, one could form neologisms to match vertical (Y), i.e.: *rougical or *gulical (X, synonyms for horizontal) and *azurical (perhaps rather *azurial, *azureal, *azural) or *bleucal (Z).

Related Systems

Fortunately, most people do not have to deal with cylindrical, polar, equatorial, horizontal or other spherical and yet more exotic coordinate systems on a regular basis. Those require terms like pole, horizon and equator, longitude and latitude, ascension and declension, azimuth, celestial, ecliptic and galactic, zenith and nadir.

  • Your upper-left xyz diagram appears to be a reflection of what it should be. – Rosie F Apr 29 at 6:47

I had this same question working on a 3D interface today, and came to the conclusion that "vertical" (y axis), "lateral" (x axis), and "horizontal" (z axis) fit reasonably well.

By deductive reasoning (taking away the left-to-right perspective covered by lateral), we can conclude that "horizontal" is an appropriate term for nearest to furthest away (toward the horizon, as it were.)

protected by RegDwigнt Feb 4 '12 at 22:26

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