In this paper, for the first time in the literature, a custom circuit is proposed to process the heavy calculations needed to change in real-time the reference coordinate system of vectors measured by tri-axial accelerometers, in order to make a pre-processing stage for the building of virtual sensors like linear and gravity accelerometers. To this purpose, a new “hardware friendly” algorithm has been derived which can be implemented in a more compact iterative structure to combine high accuracy and low power consumption, in order to conveniently integrate it into the circuitry of smart accelerometers. Synthesis with 65 nm CMOS std_cells returns a power dissipation of 0.89 μW and an area of about 0.024 mm². Results are the current state-of-the-art for this kind of applications and they are very promising for the future integration in smart sensors for wearable applications.