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40d:Z-axis
The third axis is known in math as the z-axis.
It's easy to think of a graph with an x-axis and a y-axis, right?
In the Dwarf Fortress map view, travelling east or west moves you along the x-axis, and travelling north or south moves you along the y-axis. Travelling higher or deeper moves you along the z-axis.
The z-axis, as you can see, is perpendicular to both the x-axis and the y-axis to create a 3D coordinate system, which is what Dwarf Fortress is based in.
Thus, objects described with only two axes are two-dimensional, whilst objects with depth measured along the z-axis are three-dimensional.
The z-axis is believed to be in part of the game engine that calculates accuracy of weapons based on where dwarves are, how missiles fly, and other similar considerations.[Verify]
To move up and down, use < and > (which are shift, and shift.).
In fortress mode
In fortress mode, the right-most column shows your location on the z-axis. Blue is above ground, brown is below ground, and yellow shows the current level. This reflects the elevation profile for the spot the cursor is currently over. The number at the top shows how many levels above or below the surface the spot currently is. The number at the bottom is the total elevation of the current level.