Quantifying the volumetric capability of machine tools across their working volume is a vital part of efficient precision engineering particularly when manufacturing complex geometric features. Extensive research work has previously been conducted to establish models that demonstrate the link between machine errors and deviations from specified geometric features on the workpieces. Besides an error model, an uncertainty model is also needed to quantify both the deviations and variations simultaneously, enabling more reliable evaluation of machine capability against conformity zones and identification of more effective compensation strategies for both machine manufacturers and users. Although geometric errors of individual axes are well documented, their combined effect across the working volume is still insufficiently characterised, and the associated uncertainty remains largely overlooked. Current academic and industrial practice often focuses on error identification without quantifying how measurement uncertainties propagate through a machine’s working volume. In other words, the existing research works have primarily focused either on deterministic indirect kinematic models or on deterministic diagonal measurements, while this research integrates uncertainty-aware evaluation of volumetric errors into both indirect and direct approaches within a unified framework. This reveals a clear gap: modern metrological equipment provides increasingly precise geometric measurements, yet systematic and integrated evaluation of uncertainty of machine’s volumetric performance remains largely unaddressed. Therefore, the aim of this thesis is to fill this gap by developing systematic methods for evaluating the uncertainty of volumetric errors.This thesis develops and investigates two complementary methods for examination of volumetric performance: Indirect and direct. The indirect approach uses the machine’s rigid body kinematic chain to construct an error model based on Homogeneous Transformation Matrices (HTM). This model populates measured individual geometric errors and computes a volumetric deviation vector at each coordinate point across a grid of selected target positions. Based on this error model, measurement uncertainty is quantified using two methods: the Monte Carlo Method (MCM) providing insight into probabilistic distribution of volumetric deviation vectors, and the novel Analytical Boundaries Method (ABM) computing more conservative uncertainty boundaries with significantly reduced computational effort and resources. In parallel, an enhanced direct approach was developed to overcome uncertainties from rigid body assumption. The new method builds on the diagonal tests to directly characterise volumetric performance at all measured coordinates. This direct method not only evaluates diagonal positioning deviations but also assesses two straightness deviations to fully define volumetric deviation vector. The Guide to the expression of Uncertainty in Measurement (GUM) uncertainty framework is then used to estimate their associated uncertainties. Both direct and indirect approaches represent the uncertainty of each volumetric deviation vector as a cuboidal volume aligned either with the principal axes of the machine for HTM, or with the diagonal trajectory and its two mutually perpendicular directions for the direct diagonal tests. The thesis demonstrates that from the conventional geometric measurements on a Cartesian machine tool and utilising a kinematic model such as HTM based on machine’s structural loop, volumetric deviation vectors, volumetric accuracy (ISO term), and the associated uncertainty of the volumetric deviation vectors at all measured target position can be computed along the machine’s X-, Y- and Z-axes across its working volume. Furthermore, corresponding volumetric indicators can be obtained from face and body diagonal tests along the diagonal direction (D) and two mutually perpendicular straightness directions (S1, and S2). By conducting experiments on a test Vertical Machining Centre (VMC), this research also establishes practical and systematic procedures for the evaluation of these volumetric performance indices of machine tools using both indirect modelling and direct measurement. These indices provide useful tools for uncertainty-aware characterisation of the volumetric performance of machines in a consistent and comparable manner. The thesis contributes a generic framework for evaluating the uncertainty of volumetric errors using both indirect and direct approaches applicable to machine tools regardless of configurations or kinematic chains. It demonstrates that volumetric uncertainty can be represented systematically as a cuboidal volume and efficiently quantified across the working volume. It also highlights that the performance of uncertainty models is heavily dependent on the quality of input quantities. This framework accommodates a wide range of uncertainty contributors including geometric, thermal, environmental, instrumental and mechanical factors, and is extendable to machine tools with both rigid and non-rigid behaviour. The research establishes a foundation for future improvements in error modelling, instrument capability assessment, robotic machining volumetric evaluation, and the development of future ISO standards related to volumetric performance and diagonal testing. Together, these contributions strengthen the metrological basis for uncertainty-aware performance evaluation and compensation of machine tools in industrial settings.