We present a method to determine the isotropic elastic modulus of nanometer-thick films of unknown or imprecise microstructure and composition. First, the mesoscopic stress of the film is determined using Stoney's method. Then, after fabricating film-stripes by lithography, dark-field electron holography is used to image the strain fields (3 nm spatial resolution, ∼2 × 10−4 precision) resulting from the local interactions between the stripes and an underlying silicon crystal. By comparing the experimental results with finite element method modeling, we deduce Young's modulus of the film. Silicon nitride films on Si substrates are presented as a model system.