The present disclosure provides an electrical module and a modular electrical building system including electrical modules. The electrical module includes a printed circuit board (PCB), a housing member, one or more magnets, and one or more inter-locking parts. The PCB has a top surface, a bottom surface, and opposite sides between the top surface and the bottom surface. The housing member is attached to each side of two opposite sides of the PCB and includes an opening in a bottom surface. The magnets are arranged within the housing member and are capably of magnetically attaching the electrical module to another electrical module. Each inter-locking part is configured to pass through the housing member on each side of the PCB. Each inter-locking part has a protrusion extending from a top surface of the housing member and is exposed to the opening in the bottom surface of the housing member.