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For manually operated machine tools, the accuracy of the machine tool structure limits the accuracy of the parts produced. Such is not necessarily the case with computer numerically controlled (CNC) machine tools. This concept may not be immediately obvious to the engineering undergraduate. The method of error compensation is presented here in a manner that is accessible to the undergraduate engineering student. A homogeneous transformation matrix (HTM) model quantifies the geometric errors of a machine tool, which can be compensated for in software. The mathematical treatment is reduced to only essential elements to emphasize physical understanding. A key feature of this presentation is the application of the model to a three-axis milling machine. This illustration enables the undergraduate student to grasp the concept with ease. Another feature is that the entire model is developed from first principles, which does not require the student to invoke any empirical relationships. Three solved numerical problems illustrate the application of the model to practical situations. Information provided here may be used by the teacher as a template to introduce this subject at the undergraduate level.