Many papers have been published on methods to determine the normal spring constant, kz, of atomic force microscope (AFM) cantilevers. This is necessary to calibrate force measurements in the AFM, which then lead to a wide variety of applications from measuring the rupture force of protein bonds to determining the Young's modulus of materials such as polymers at surfaces. Manufacturers' nominal values of kz have been found to be up a factor of two in error, therefore practical methods to calibrate kz are required. There are three main categories of methods, with some overlap, which we call: (1) dimensional, (2) static experimental and (3) dynamic experimental. Here, we consider the dimensional aspects of these methods involving the cantilever material properties and geometry. We do this via reviewing the analytical equations of seven publications and comparing them with finite element analysis (FEA) calculations. It is shown that the best analytical equations are those of Neumeister and Ducker but that these need a revision for the bending of the triangular portion of the V-shaped cantilever. This is done and the correlation with FEA is then excellent. Equations are also provided for the effect of a metallized layer and the imaging tip not being at the cantilever apex; these also agree with FEA. We evaluate the relevant uncertainties and provide recommendations as to the best equations to use together with relevant correction parameters based on the assumption that the FEA calculations are valid. We test this assumption elsewhere.
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