All these locations, horizontal, vertical, and height are defined from the same 'Zero Location'. Each 'axis vector' begins at this zero location and has a positive direction and a negative direction.

You can use your left hand to imitate the orientation of the cartesian coordinate system used by most CAD/CAM applications and CNC machines. When you extend your thumb straight up, it is pointing in the positive Z direction. Point straight ahead with your index finger, you are pointing towards the Y positive direction. Now bend your middle finger 90 degrees. Your middle finger is pointing towards the X positive direction!

What this means is any location can be defined by a coordinate relative to that 'Zero Location' we discussed earlier, horizontally (X), vertically (Y), and height-wise (Z). Watch the illustration to the right to see how a square is created using positive and negative'-' X and Y values for it's endpoints. In this example all the Z values remain at zero.

Most likely, your CNC machines use this same coordinate system although some machines use this coordinate system as if you were looking at the directions from the back of the machine.

For the Z coordinate, just remember that when a positive Z is programmed, the tool moves away from the table and the part you are cutting. Programming a negative Z brings the tool closer to the table and towards the part you intend to machine.