Most ultrasound (US) imaging techniques use spatially-constant speed-of-sound (SoS) values for beamforming. Having a discrepancy between the actual and used SoS value leads to aberration artifacts, e.g., reducing the image resolution, which may affect diagnostic usability. Accuracy and quality of different US imaging modalities, such as tomographic reconstruction of local SoS maps, also depend on a good initial beamforming SoS. In this work, we develop an analytical method for estimating mean SoS in an imaged medium. We show that the relative shifts between beamformed frames depend on the SoS offset and the geometric disparities in transmission paths. Using this relation, we estimate a correction factor and hence a corrected mean SoS in the medium. We evaluated our proposed method on a set of numerical simulations, demonstrating its utility both for global SoS prediction and for local SoS tomographic reconstruction. For our evaluation dataset, for an initial SoS under- and over-assumption of 5% the medium SoS, our method is able to predict the actual mean SoS within 0.3% accuracy. For the tomographic reconstruction of local SoS maps, the reconstruction accuracy is improved on average by 78.5% and 87%, respectively, compared to an initial SoS under- and over-assumption of 5%.