A novel two-parameter area function for determination of near surface properties of Young’s modulus of elasticity and hardness has shown promise for compensating for the imperfection of the tip-end in an instrumented indentation measurement. This paper provides a comprehensive study involving a Berkovitch tip. The tip is utilized in an MTS nanoindentation measurement machine and is used to establish load indentation information for fused silica samples. The geometry of the tip is then characterized independently using a highly accurate atomic force microscope. Using the indentation data along with the two-parameter area function methodology, the tip-end radius of curvature is found to provide the most consistent value of modulus of elasticity. Independently, the data from the scanning electron microscope measurement of the same tip is used to obtain the least-squares estimation of the tip curvature. The two approaches yield favorable agreement in the estimation of tip-end radius of curvature. Therefore, the validity of the two-parameter area function method is proved. The method is shown to provide a robust, reliable, and accurate measurement of modulus of elasticity and hardness in the nanoscale proximity of a surface.