In this paper, we propose a dipole coupled magnetic quantum-dot cellular automata-based approximate nanomagnetic (APN) architectural design approach for subtractor and adder. In addition, we also introduce an APN architecture which offers runtime reconfigurability using a single design layout comprising only four nanomagnets. Subsequently, we propose the APN add/sub architecture by exploiting shape anisotropy and ferromagnetically coupled fixed input majority gate. The proposed APN architecture designs have been implemented using a micromagnetic simulation tool and performance has been compared with the state-of-the-art approach resulting in a ∼50%-80% reduction in the number of nanomagnets and clock cycles without degradation in the accuracy leading to area and energy efficiency. © 2019 IOP Publishing Ltd.