Integrin-mediated cell adhesion plays a critical role in cell migration, proliferation, signaling and survival. A number of diseases, including several cancers, show increased integrin activation that ultimately lead to metastasis. Unfortunately, computational models of adhesion have traditionally been at the continuum level and have ignored molecular thermodynamic aspects of cell adhesion. In order to overcome these critical gaps in our understanding of cell adhesion, we present a model based on single chain mean field thermodynamics. Our model is independent of cellular geometry and can quantify cell matrix interactions of cells cultured in two and three dimensional environments. By incorporating the conformational preferences and restrictions of the molecules, solvation effects as well as long and short-range interactions, we are able to predict adhesive force and free energy as a function of a number of key variables such as surface coverage, interaction distance, molecule size and solvent conditions. Our method allows us to compute the free energy and force of adhesion in a multi-component system, where we can simultaneously study integrins and ligands of different sizes, chemical identities and conformational properties. The results of our simulations show good agreement with experiments and not only provide a fundamental understanding of adhesion at the molecular level but also suggest possible strategies for designing the next generation of biomaterials.