A method to determine the van der Waals forces from phase-distance curves recorded by atomic force microscopy (AFM) in tapping mode is presented. The relationship between the phase shift and the tip-sample distance is expressed as a function of the product of the Hamaker constant by tip radius. Silica-covered silicon tips are used to probe silica-covered silicon substrate in dry conditions to avoid capillary effects. Tips being assumed spherical, radii are determined in situ by averaging profiles recorded in different directions on hematite nanocrystals acting as nanotemplates, thus accounting for tip anisotropy. Through a series of reproducible measurements performed with tips of various radii (including the in-situ characterization of a damaged tip), a value of (6.3 +/- 0.4) x 10(-20) J is found for the Hamaker constant of interacting silica surfaces in air, in good agreement with tabulated data. The results demonstrate that the onset of the tip-surface interaction is dominated by the van der Waals forces and that the total force can be modeled in the framework of the harmonic approximation. Based on the tip radius and the Hamaker constant associated to the tip-substrate system, the model is quite flexible. Once the Hamaker constant is known, a direct estimate of the tip size can be achieved whereas when the tip size is known, a quantitative evaluation of the van der Waals force becomes possible on different substrates with a spatial resolution at the nanoscale. (C) 2012 Elsevier By. All rights reserved.