The detailed isothermal electrochemical model for a lithium ion cell has ten coupled partial differential equations to describe the cell behavior. In an earlier publication [Journal of Power Sources, 222, 426 (2013)], a reduced order model (ROM) was developed by reducing the detailed model to a set of five linear ordinary differential equations and nonlinear algebraic expressions, using uniform reaction rate, volume averaging and profile based approximations. An arbitrary current profile, involving charge, rest and discharge, is broken down into constant current and linearly varying current periods. The linearly varying current period results are generic, since it includes the constant current period results as well. Hence, the linear ordinary differential equations in ROM are solved for a linearly varying current period and an explicit algebraic algorithm is developed for lithium ion cell voltage prediction. While the existing battery management system (BMS) algorithms are equivalent circuit based and ordinary differential equations, the proposed algorithm is an explicit algebraic algorithm. These results are useful to develop a BMS algorithm for on-board applications in electric or hybrid vehicles, smart phones etc. This algorithm is simple enough for a spread-sheet implementation and is useful for rapid analysis of laboratory data.