This paper describes a mathematical investigation of the relationship between wear volume, wear depth and wear direction in acetabular components. The analysis takes into account the cylindrical and conical portions at the mouth of certain types of socket and also incorporates the effect of an initial radial discrepancy between the femoral head and socket. Published formulae for converting linear wear measurements to wear volumes are shown to be incorrect. Wear volume is shown to be highly dependent on the wear direction, increasing by more than 90 per cent over a 60° range. Cylindrical and conical portions of a 22.225 mm cup may contribute up to about a third as much wear as the hemispherical socket. At low wear depths, the neglect of a radial discrepancy between the components can result in an overestimation of wear volume in excess of 100 per cent.
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