Purpose - The purpose of this paper is to calculate forces between rectangular conductors with a uniform current density as can be found in the long coils as used in linear actuators and planar motors. Design/methodology/approach - The proposed methodology relies on a single analytical equation that is used to compute all the force components. Findings - Several comparisons with other available techniques are provided. All the comparisons confirm the validity of the proposed analytical method. Originality/value - In the literature, other analytical methods for the force computation can be found. However, these often have limitations (e.g. only adjacent conductors or non-adjacent conductors). This paper adds a new compact expression that covers all the possible configurations at the same time. This new tool holds for all the analytical expression found in the literature.