General · Fundamentalsbeginner~2 min read

X, Y and Z: how the machine describes space

Short answer

X is left and right. Y is front and back. Z is up and down. On a router, positive Z is up and away from the material, so nearly all cutting happens at negative Z values, below the zero you set.

The three directions

Stand in front of the machine, the way you normally would to load a piece of wood.

X axis

Left and right. Positive X is to your right.

Y axis

Toward and away from you. Positive Y is away, toward the back.

Z axis

Up and down. Positive Z is up.

Most hobby gantry machines move the tool in X and Z, and move either the gantry or the table in Y. It does not matter mechanically which part moves. The coordinate system always describes where the tool is relative to the work, so if the table moves toward you, the software still calls that the tool moving in positive Y.

Why Z is the one to respect

X and Y mistakes usually make a bad part. Z mistakes break things. Almost every expensive beginner accident is a Z problem:

Z zero set to the spoilboard when the file expected the top of the material, so the first plunge goes an inch too deep.
Z zero set to the top of the material when the file expected the spoilboard, so the cut floats above the wood and does nothing.
A rapid move across the work at a Z height lower than a clamp.
The bit slipping down in the collet mid-job, which quietly moves Z zero for the rest of the cut.

Positive Z is safety

Any time you are unsure what the machine is about to do, raise Z. A tool in the air cannot ruin anything. This is also why the first move of most programs is a rapid to a safe Z height before anything else happens.

Signs, and why your cut depths are negative

You set Z zero at the top of your material. Everything below that top surface is negative. So a pocket 0.25 inches deep is cut at Z minus 0.25. If you see a toolpath that wants to cut at positive Z, either the zero is set somewhere other than the top of the stock, or something is wrong with the file.

This is also why safe Z and clearance height are positive numbers. They are distances above your zero, which is usually above your material.

The fourth axis, briefly

Some machines add a rotary axis, usually called A, which spins a workpiece under the tool so you can carve round objects like table legs or baseball bats. It is a genuine expansion of what the machine can do, and it is a topic for later. Nothing in the first year of CNC needs it.

Checking your machine agrees with you

Jog the machine a small amount in positive X and watch which way the tool goes. Then positive Y. Then positive Z. If any of them goes the wrong way, the motor direction is inverted in the controller configuration, and everything you cut will be mirrored or upside down in that axis. Fix it in the configuration, not by mirroring your designs, or you will spend the next year confused.