This paper offers a two-zone, physical, N O x model with low computational cost, suitable for vehicle on-board, implementation. The paper introduces a model which is able to compute N O x emission formation with high time resolution during an engine cycle. The physical background is described as well as the equations upon which the model is based. The model was developed with a structure suitable for implementation in embedded systems. Large parts of the effort has been devoted to develop an algorithm implementing the described physical model and techniques used and issues encountered are described in the paper. Ease in computation has been a top priority, making the algorithm implementation feasible in some sort of embedded system, e.g. embedded processor or embedded electronic hardware (FPGA). For the sake of implementation, parts of the algorithm had to be pre-computed and stored in tables, allowing significant acceleration of the computations. Since the model is non-linear, exponentially spaced tables had to be developed in order to successfully tabulate the parts needed without consuming too much memory. The outcome regarding number of operations, memory requirement and feasible computation speed are discussed. The final result is a low-cost N O x algorithm (implementing a physical N O x model) which is able to compute several orders of magnitude faster than the N O x models known so far.