The formation and shape variation of the Hawaiian plume swell is re-examined numerically. Scaling laws for the plume buoyancy flux and swell width and height help gaining new insight in relationships between swell formation and relevant model parameters, like plume temperature and size, and mantle rheology. A scaling law for the plume buoyancy F = Aη0-1.2Rp3.5ΔTp2.2 exp(1.3 ¿ 10-8EΔTp), with background mantle viscosity η0, plume radius Rp, plume excess temperature ΔTp, and activation energy E fits numerical flux measurements within 8%. Scaling laws for the swell width and height have similar forms, and their multiplication resembles the buoyancy flux scaling law within 10%. These scaling laws suggest that the background mantle viscosity plays a significant role, and that the increased Hawaiian plume intensity ~25 Ma ago is due to a plume excess temperature increase of 50%.