The growing concerns posed by orbital debris represent a serious threat to the future of space operations in low Earth orbit. With the goal of limiting the formation of new debris, space agencies are proposing international guidelines that satellites should be able to deorbiting within 25 years of the end of their operational life. Orbital decay is typically caused by atmospheric drag, so estimating the decay time of a satellite subject to drag is critical to assessing whether the guidelines are met. However, such estimate is a very challenging task because of the difficulty of accurately modeling atmospheric properties and because of the coupling of orbital dynamics with spacecraft attitude. In this paper, a simplified algorithm based on the King-Hele formulation is proposed to rapidly estimate the decay time of an orbiting satellite without imposing any assumptions on the spacecraft’s nominal size, mass, geometry or attitude. The algorithm accounts for the effect of solar activity level variations on atmospheric properties and drag coefficient through an iterative procedure and can be applied to any object in orbit. Numerical tests show that the predictions in terms of decay times are very accurate for satellites that are quite different in size and geometry, including the presence of an aerodynamic drag augmentation system such as a drag sail.