The deterministic errors of an accelerometer comprise the prevailing i) bias, ii) scale factor, and iii) non-orthogonality. Together, these errors result in a nonlinear measurement model, which is conventionally solved via an iterative nonlinear least-squares method. In contrast to the conventional approach, we propose a novel method to transform the above nonlinear model into a system of linear equations, resulting in an exact, closed-form solution of the deterministic errors. The developed mathematical formulations are first verified in a simulation set-ting, followed by a real-time implementation using Robot Operating System for small micro-electromechanical inertial measurement units.