The origin of the pseudogap and its relationship to symmetry-broken orders in cuprates have been extensively debated. Here, we report a unified energy law underlying the pseudogap, which determines the scattering rate, pseudogap energy, and its onset temperature, with a quadratic scaling of the wavevector of density wave order (DWO). The law is validated by data from over one hundred samples, and a further prediction that the master order of pseudogap transforms from fluctuating spin to charge DWO is also confirmed by independent measurements. Furthermore, the energy law enables our derivation of the well-known linear scalings for the resistivity of the strange metal phase and the transition temperature of the superconducting phase, shedding light on the universal origin of various phases. Finally, it is concluded that fluctuating orders provide a critical bridge linking microscopic spectra to macroscopic transport in cuprates, showing promise for the quantification of other strongly correlated materials.