  Spectroscopic reverberation mapping (RM) is a direct approach widely used to
estimate the mass of black holes (BHs) in active galactic nuclei (AGNs).
However, it is very time consuming and difficult to apply to a large AGN
sample. The empirical relation between the broad-line region size and
luminosity (H$\beta$ $R_{\rm BLR}\unicode{x2013}L$) provides a practical
alternative yet is subject to large scatter and systematic bias. Based on the
relation between the continuum emitting region size and luminosity ($R_{\rm
CER}\unicode{x2013}L$) reported by Netzer (2022), we present a new BH mass
estimator via continuum RM (CRM) by comparing $R_{\rm CER}$ and $R_{\rm BLR}$,
assuming that the continuum lags are dominated by the diffuse continuum
emission. Using a sample of 21 AGNs, we find a tight $R_{\rm
BLR}\unicode{x2013}R_{\rm CER}$ relation (scatter$\sim$0.28 dex) and that
$R_{\rm BLR}$ is larger than $R_{\rm CER}$ at 5100 \r{A} by an average factor
of 8.1. This tight relation enables the BH mass estimation based on the CRM
combined with the velocity information. Applying the relation to rest objects
in our CRM sample, we demonstrate that the predicted $R_{\rm BLR,CRM}$ follows
the existing H$\beta$ $R_{\rm BLR}\unicode{x2013}L$ relation well and the
estimated CRM BH masses are consistent with the RM/single-epoch BH masses using
H$\beta$. This method will provide significant applications for BH mass
estimation thanks to the short continuum lags and the easily accessible
high-cadence, large-area photometric data, especially in the era of Legacy
Survey of Space and Time.
