Establishing a link between atomistic processes and battery cell behavior is a major challenge for lithium ion batteries. Focusing on liquid electrolytes, we describe parameter-free molecular dynamics predictions of their mass and charge transport properties. The simulations agree quantitatively with experiments across the full range of relevant ion concentrations and for different electrolyte compositions. We introduce a simple analytic form to describe the transport properties. Our results are used in an extended Newman electrochemical model, including a cell temperature prediction. This cross-scale approach provides quantitative agreement between calculated and measured discharge voltage of a battery and enables the computational optimization of the electrolyte formulation.