A CNC Router operates in a 3D universe. When you draw a shape on a piece of paper, you are creating a 2D image.  When you cut the shape out, you are working in 2.5D.  When you carve a shape with height, width and depth, you are working in 3D. 

CNCs use coordinate systems represented as different axes to understand 2.5D and 3D space. The X, Y, and Z axes define the coordinate space within the cutting area of the machine. Each axis can be represented as a number line. Every number line has an origin (zero point) with positive and negative measurements, as shown.


When the number lines of two axes intersect at a common zero point, they create four quadrants.  The coordinates in the first quadrant are all positive making it the easiest quadrant to work with.  In the illustration the X and Y axis are determined by how they relate to each other in the right-hand coordinate system.

Right Hand Coordinate System

To visualize the right-hand coordinate system, hold your right hand out with your index finger sticking straight out like the barrel of a gun with your thumb pointing straight up.  As you point your finger away hold your middle finger at 90 degrees, (pointing to the left).  The thumb pointing straight up represents the Z-axis, the index finger the X-axis, and the middle finger the Y-Axis. In the right-hand coordinate system, a clockwise rotation around the Z-axis will cross the X-axis first and then the Y-axis. The right-hand coordinate system is commonly used with CNC Routers.


The cutting area of a CNC Router is like a cube.  Each side of the cube is a plane made up of two axes, X-Y, Y-Z, or X-Z. The CNC uses coordinates to describe space within the cutting volume.

The position of a CNC Router bit in the cutting area is describe by its position within those three planes.

Machine Coordinates.

There are two coordinates you need to be familiar with, machine coordinates and workpiece coordinates.  Machine coordinates refer to the travel limits of the machine’s three axes.  In some CNCs, those travel limits are designated with limit switches that are activated any time the router or spindle attempts to move beyond any of those physical limits.

A triggered limit switch indicates that the work piece was not correctly oriented within the machine’s cutting area.  When that happens, the placement of the workpiece must be corrected. The CNC must be homed to re-sync the machine to the workpiece.

BobsCNC uses “soft” limits which are programmed into the firmware on the Controller.  After the CNC is homed the controller remembers the home location and calculates the distance the spindle can travel compared to the soft limits.

Workpiece Coordinates.

Workpiece coordinates are set when the toolpath is created.  The two most common zero points are set in the lower left-hand corner or the center of the workpiece, though it can be placed anywhere you choose.