Error correction of measurements of workpieces taken using a coordinate positioning apparatus in which the workpiece is mounted on a bed of the apparatus and a workpiece sensing probe is moved relative to the bed into a position sensing relationship with each workpiece and a position reading taken, and in which means are provided for measuring at least a function of the acceleration of the probe relative to the bed, the method including, in any suitable order: measuring the workpiece; determining the repeatable measurement errors from a predetermined error function, look-up table or map; measuring at least a function of the acceleration and calculating the unrepeatable measurement errors as the workpiece is measured; and combining the repeatable and non repeatable errors in steps (b) and (c) to determine the total errors; and using the total errors determined in step (d) to correct the measurements of the workpiece.