Coordinates for the CNC Mill 222

"Coordinates for the CNC Mill" provides an overview of the coordinates used to program cutting operations on CNC mills or machining centers. It introduces the systems of both Cartesian and polar coordinates and explains the Cartesian axes for vertical and horizontal CNC mills. The class describes how coordinates are used on blueprints and applied as machine movements. This includes concepts such as incremental vs. absolute coordinates, linear and circular interpolation, machine zero, and program zero.

Coordinates and axis movements are at the core of operations for a CNC machine. A foundational knowledge of these topics is necessary to understand how and why parts can be successfully made on the CNC mill or machining center.

Class Details

Class Name:
Coordinates for the CNC Mill 222
Number of Lessons:

Class Outline

  • CNC Coordinates for the Mill
  • The Cartesian Coordinate System
  • Blueprints and Coordinates
  • Blueprints and Coordinates
  • Polar and Spherical Coordinates
  • Coordinate Basics
  • Axis Locations
  • Axes on the Vertical CNC Mill
  • Axes on the Horizontal CNC Mill
  • Rotational Axes
  • Axes on Machining Centers
  • Machining Center Axes
  • Contouring
  • Machine Zero and Program Zero
  • Incremental and Absolute Coordinates
  • Incremental and Absolute Coordinates in Action
  • Machine Movement Review


  • Describe the Cartesian coordinate system.
  • Identify the axes and origin of the Cartesian coordinate system.
  • Describe the relationship between blueprints and coordinates.
  • Describe polar and spherical coordinates.
  • Describe the general guidelines for the locations of axes on CNC machines.
  • Identify the X, Y, and Z axes on a vertical CNC mill.
  • Identify the X, Y, and Z axes on a horizontal CNC mill.
  • Identify the A, B, and C rotational axes.
  • Describe cutting tool positions and movements associated with axes on the machining center.
  • Describe contouring.
  • Describe machine zero and program zero.
  • Compare incremental and absolute coordinates.

Job Roles


  • CNC Milling Programming, Setup, & Operation
  • CNC Milling: Programming, Setup, and Operations-FastTrack


Vocabulary Term Definition
A axis A rotational axis that describes motion around, or about, the X axis centerline. The A axis allows complex workpiece movement on the mill.
absolute coordinates A series of numerical positions calculated from a fixed, constant point of origin. Absolute coordinates are very accurate and are thus commonly used.
angles A figure formed by the intersection of two lines. Angles are also used to measure distances around a circle.
axes Imaginary lines that pass through the center of a point or object. Axes are used to describe the positions of objects on the Cartesian coordinate system.
B axis A rotational axis that describes motion around, or about, the Y axis centerline. The B axis allows complex workpiece movement on the mill.
blueprint A design representing the dimensions of a specific workpiece. Blueprints are used to create part programs.
C axis A rotational axis that describes motion around, or about, the Z axis centerline. The C axis describes either the rotation or the positioning of the cutting tool.
Cartesian coordinate system The system that describes the position of any point or object in three-dimensional space by numerically expressing its distance from a fixed position along three linear axes. The Cartesian coordinate system is used to describe measurements in CNC milling and turning.
circular interpolation A circular cutting path that requires tool motion on multiple axes. Circular interpolation is used to create curved shapes.
CNC Computer numerical control. A programmable control system for a machine tool, directed by mathematical data, which uses microcomputers to carry out various machining operations. CNC milling is much quicker and more precise than its manual counterpart.
CNC mills A milling machine that is controlled by a computer running programs driven by numerical data. CNC mills are much more precise than their manual counterparts.
computer-aided design CAD. The use of computers for the design and drawing of a part or other product. Computer-aided design drawings are automated and precise.
contouring Tool movement along two or more axes simultaneously. Contouring is used to create curved, non-linear features.
cutting tool A device with one or more edges used to create chips and remove metal. Cutting tools are either single-point or multi-point tools.
horizontal CNC mill A mill with a spindle that is parallel to the ground and a worktable that is positioned vertically. A horizontal CNC mill approaches the workpiece from the left or right.
incremental coordinates A series of numerical positions that use each current position as the origin for the next position. Incremental coordinates can pass errors from position to position, which makes them less reliable than absolute coordinates.
linear Extending indefinitely along a straight line. Linear axes are used to describe the Cartesian coordinate system.
linear interpolation A movement along two or more axes simultaneously that creates a straight line. Linear interpolation is used to cut curves or contours.
machine zero The zero position that is permanently set by the manufacturer of each particular CNC machine. Machine zero is typically used for loading and unloading parts.
offset A numerical value stored in the CNC control that repositions machine components. Offsets are used to adjust for differences in tool geometry, part size, tool wear, and any other changing variables that may affect the manufacture of the part.
origin A fixed, central point in the Cartesian coordinate system. The origin has a numerical value of zero.
part program A series of numerical instructions or commands that direct a CNC machine to perform the necessary sequence of operations to set program zero from machine zero and to machine specific workpiece features. Multiple part programs can be stored in a CNC machine at the same time.
part programmer The person responsible for the creation of a part program. The part programmer translates the workpiece design into program instructions for the CNC mill.
polar coordinate system A system that describes positions in three-dimensional space using locations on a sphere or ball. The polar coordinate system uses the angle of an object's location to describe it.
program zero The position that acts as the origin for the part program of a particular workpiece. Program zero is unique to each workpiece design and is selected by the part programmer.
right angles An angle formed by two lines that are perpendicular to one another. Right angles exist at the corners of squares or rectangles.
right-hand rule A quick reference that shows the location of the X, Y, and Z axes. A person displays his or her right hand, and the first three fingers from the right each represent the X, Y, and Z axis in order.
rotational axes The axes that describe turning or rotation around, or about, the linear axes. The rotational axes are the A, B, and C axes.
sphere A perfectly round three-dimensional object. The sphere is the basis for the spherical coordinate system.
spherical coordinate system A coordinate system which locates points based on their angles from two of the three axes as well as distance from the origin. The spherical coordinate system can be useful for circular or spherical parts.
spindle The main component of the machine tool that rotates. On the CNC mill, the spindle holds the cutting tool.
three-dimensional An object which has length, width, and depth. Three-dimensional objects can be represented by the spherical coordinate system or Cartesian coordinate system.
two-dimensional An object which has length and width but not depth. Two-dimensional coordinates can be represented using the polar coordinate system or Cartesian coordinate system.
vertical CNC mill A mill with a spindle that is positioned vertically over a worktable parallel to the floor. Vertical CNC mills match the right-hand rule, meaning that the Z axis is vertical, X axis horizontal moving from left to right, and Y axis horizontal moving forward and away.
workpiece A part or component that is being worked on. Workpieces in CNC machines are the raw materials that are shaped by the machine.
worktable The table that supports a workpiece during a manufacturing operation. Workpieces are generally rigidly held to the worktable using workholding devices.
X axis A linear axis in the Cartesian system that is perpendicular to the Z and Y axes. On a CNC mill, the X axis often describes the longest distance of travel parallel to the worktable.
Y axis A linear axis in the Cartesian system that is perpendicular to the Z and X axes. On a CNC mill, the Y axis often describes the shortest distance of travel parallel to the worktable.
Z axis The linear axis that represents motions and positions perpendicular to the worktable or machine bed. On a CNC mill, the Z axis is always parallel to the spindle.