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The minimization of sources of uncertainty in nanoindentation experiments is crucial for accurate determination of nanomechanical properties. A common source of uncertainty in these measurements is the estimation of tip shape and size. Besides the experimental determination of the indenter's real geometry, determination of the instrument's compliance is also necessary. We use an atomic-force-microscope-based procedure for the determination of nanoindentation tip parameters needed to account for errors induced by tip shape nonideality and to permit the evaluation of the relative contributions of the instrumental errors associated with the experimentally determined values of hardness and modulus. We compare the definitions of the currently used tip shape area function based on physically relevant parameters with the scan and propose a hyperbolic definition that meets all physically relevant criteria while being simple enough to yield good results with numerical nonlinear fitting routines.