Detecting relative rather than absolute changes in external signals enables cells to make decisions in fluctuating environments and diverse biological contexts. However, how mammalian signaling networks store the memories of past stimuli and use them to compute relative signals is not well understood. Using the growth factor-activated PI3K-Akt signaling pathway, we develop computational and analytical models, and experimentally validate a novel mechanism of relative sensing in mammalian cells. This non-transcriptional mechanism relies on a new form of cellular memory, where cells effectively encode past stimulation levels in the abundance of cognate receptors on the cell surface. We show the robustness and specificity of the relative sensing for two physiologically important ligands, epidermal growth factor (EGF) and hepatocyte growth factor (HGF), and across wide ranges of background stimuli. The described memory and sensing mechanism could play a role in multiple other sensory cascades where stimulation leads to a proportional reduction in the abundance of cell surface receptors.