In the early 1990s the Americans introduced diagonal laser tests as a quick method for evaluating the volumetric accuracy of machine tools. More recently, IS0 have started preparing a new standard based on this document. This paper examines what can be achieved with this type of test, and what advantages can be gained by carrying out the proposed additional face diagonal measurements in a three-dimensional domain. Of particular interest is the potential ability for checking squareness measurements on large machmes. 1 Different approaches to the measurement of accuracy When a customer asks a manufacturer how accurate his machine tool will be, what he really wants to know is, how accurately will the machine produce his components. For this, all he needs to know is how accurately the tool to workpiece relationship can be maintained. The manufacturer will probably evade the issue by producing a test document showing the accuracy of squareness between the axes, the positioning accuracy of each separate axis along a straight line, the run-out of the spindle and an impressive list of other similar test measurements. Furthermore, he will probably be able to quote chapter and verse of the standard that he has based his tests on. Users of machines do not usually confine themselves to single axis movements. If a work-piece has two holes in it that do not lie along a particular axis this will require a vector move involving two or even three axes. But the likely error in position here-the centre distance error-is not readily available from the results of the manufacturer's conventional machine tests. One of the problems of defining the accuracy of a machine tool is thus finding a measurement quantity that gives the customer precisely what he needs. The tests we derive-and subsequently create standards for-are, quite rightly, Transactions on Engineering Sciences vol 34, © 2001 WIT Press, www.witpress.com, ISSN 1743-3533