In material science, bioengineering, and biology, thin liquid films and soft matter membranes play an important role in micro-lubrication, ion transport, and fundamental biological processes. Various attempts have been made to characterize the elastic properties, such as Young's modulus, of such films using Hertz theory by incorporating convoluted mathematical corrections. We propose a simple way to extract tip-size independent elastic properties based on stiffness and force measurement through a spherical tip on a flat surface. Using our model, the Young's modulus of nanoconfined, molecularly-thin, layers of a model liquid TEHOS (tetrakis 2-ethylhexoxy silane) and water were determined using a small-amplitude AFM. This AFM can simultaneously measure the stiffness and forces of nanoscale films. While the stiffness scales linearly with the tip radius, the measured Young's modulus essentially remains constant over an order of magnitude variation in the tip radius. The values obtained for the elastic modulus of TEHOS and water films on the basis of our method are significantly lower than the confining surfaces' elastic moduli, in contrast with the uncorrected Hertz model, suggesting that our method can serve as a simple way to compare elastic properties of nanoscale thin films as well as to characterize a variety of soft films. In addition, our results show that the elastic properties (elastic modulus) of nanoconfined liquid films remain fairly independent of increasing confinement.