It is recognised that profiling techniques have been widely used in industry and academic research for manufacturing control and functional control of surface roughness, in some cases, however, the profiling techniques and two-dimensional (2D) parameters defined in standards are inadequate and/or unsuitable for characterising surfaces. In recent years, there has been an increasing need for the characterization of surface topography in three dimensions (3D). Therefore a clearly defined, effective and widely accepted 3D parameter set is urgently required. Based on an understanding of intrinsic properties of surface topographic features and parameters, a primary 3D parameter set is proposed in the last two parts of this series of reports. Some of the parameters included in the primary parameter set are extended from their 2D counterparts; others are specifically defined for characterising 3D surface topography. Evidence is given to support the reasons for inclusion of each parameter in the set. In this paper, the definitions and algorithms of amplitude and some functional parameters are presented. The feasibility in terms of sampling conditions, and the application scope of the parameters is discussed. Not only is the mathematical/statistical background of the parameters presented but also experimental results obtained by testing a wide range of engineered surfaces are provided to justify the proposal. The lessons (parameter rash, correlation of the parameters) obtained in defining 2D parameters are taken into consideration in defining 3D parameters.