This work focuses on active galactic nuclei (AGNs) and on the relation between the sizes of the hot dust continuum and the broad-line region (BLR). We find that the continuum size measured using optical/near-infrared interferometry (OI) is roughly twice that measured by reverberation mapping (RM). Both OI and RM continuum sizes show a tight relation with the Hβ BLR size, with only an intrinsic scatter of 0.25 dex. The masses of supermassive black holes (BHs) can hence simply be derived from a dust size in combination with a broad line width and virial factor. Since the primary uncertainty of these BH masses comes from the virial factor, the accuracy of the continuum-based BH masses is close to those based on the RM measurement of the broad emission line. Moreover, the necessary continuum measurements can be obtained on a much shorter timescale than those required monitoring for RM, and they are also more time efficient than those needed to resolve the BLR with OI. The primary goal of this work is to demonstrate a measuring of the BH mass based on the dust-continuum size with our first calibration of the RBLR-Rd relation. The current limitation and caveats are discussed in detail. Future GRAVITY observations are expected to improve the continuum-based method and have the potential of measuring BH masses for a large sample of AGNs in the low-redshift Universe.

GRAVITY is developed in a collaboration by the Max Planck Institute for Extraterrestrial Physics, LESIA of Observatoire de Paris/Université PSL/CNRS/Sorbonne Université/Université de Paris and IPAG of Université Grenoble Alpes/CNRS, the Max Planck Institute for Astronomy, the University of Cologne, the CENTRA - Centro de Astrofisica e Gravitação, and the European Southern Observatory.