Fractals can be extremely useful when applied to tribology. Obtaining fractal descriptions of engineering surfaces and wear particles requires surface topography information to be measured, digitized and processed. Such procedures can be rigorous. This article compares various methods to calculate profile and surface fractal dimension. Profile fractal dimension is computed using three available methods, corresponding to the yard-stick, the power spectrum and the structure function method. The precision of the three methods is analyzed and compared in this paper. Surface fractal dimension is calculated using the slit island and the box counting method. Both profile fractal dimension and surface fractal dimension are used to describe TiN coating surfaces and wear particles.