Scaling laws are used when the size of a certain machine design with known performance needs to be adjusted for a new application with known requirements, or when a machine design is geometrically scaled and one needs to determine its performance. Scaling laws derived in this study allow one to quickly and accurately recalculate parameters of a geometrically scaled permanent magnet machine. They basically consist of two separate important scaling procedures: axial scaling and radial scaling. The third and inevitable scaling procedure is rewinding, which is used to adjust the winding for a required voltage level. Exact but simple analytical equations for the various parameters (torque, power, losses, mass, resistance, inductance, efficiency etc.) of the machine are derived using three independent scaling factors, one for each scaling procedure. Special attention is given to the inclusion of end-winding influence and three-dimensional permanent magnet loss effects. Algorithms for fast determination of winding parameters for a given voltage and fast determination of scaling factors for scaling based on the torque requirement with stack length limitation are presented. All derived scaling equations are numerically validated using two state-of-the-art motor design software packages with automated extraction of parameters based on finite-element calculations.