Lipids and several specialized proteins are thought to be able to sense the curvature of membranes (MC). Here we used quantitative fluorescence microscopy to measure curvature-selective binding of amphipathic motifs on single liposomes 50-700 nm in diameter. Our results revealed that sensing is predominantly mediated by a higher density of binding sites on curved membranes instead of higher affinity. We proposed a model based on curvature-induced defects in lipid packing that related these findings to lipid sorting and accurately predicted the existence of a new ubiquitous class of curvature sensors: membrane-anchored proteins. The fact that unrelated structural motifs such as alpha-helices and alkyl chains sense MC led us to propose that MC sensing is a generic property of curved membranes rather than a property of the anchoring molecules. We therefore anticipate that MC will promote the redistribution of proteins that are anchored in membranes through other types of hydrophobic moieties.