An attempt to characterise the abrasivity of a particle's geometry using a numerical descriptor, the 'spike parameter', is described in this paper. The 'spike parameter' is a measure of a particle's abrasivity and is based on representing the projected particle boundary by triangles at many scales. The calculation of the parameter involves measuring the perpendicular height and sharpness (apex angle) of all positive (i.e. convex) triangles in the particle boundary at different scales. This produces a multi-scale measure of particle 'spikiness'. In this work seven different mineral abrasives were used in two-body abrasive wear experiments. Special abrasive disks were constructed from each of the abrasive types and used in the tests. Initially aluminium and brass were used as counter sample materials. Later chalk was used as the counter sample in order to provide 'pure' abrasive wear, without grit damage or adhesion of wear debris to the surface of the abrasive disk. For each of the abrasives the 'spike parameter' was calculated. An excellent correlation between wear rates and the newly developed 'spike parameter' was found.