This brief paper describes the time evolution of three key parameters of frost accretion on flat surfaces: thickness, density, and accumulated mass. A scale analysis is conducted based on energy and mass balances on and within a mature frost layer subjected to frost growth and densification, revealing that both frost thickness and density obey the square-root-of-time rule typical of diffusive-dominant problems in transport phenomena. As a consequence, the accumulated frost mass varies linearly with time. The results have been corroborated with experimental data.