  The broad line region (BLR) size-luminosity relation has paramount importance
for estimating the mass of black holes in active galactic nuclei (AGNs).
Traditionally, the size of the H$\beta$ BLR is often estimated from the optical
continuum luminosity at 5100\angstrom{} , while the size of the H$\alpha$ BLR
and its correlation with the luminosity is much less constrained. As a part of
the Seoul National University AGN Monitoring Project (SAMP) which provides
six-year photometric and spectroscopic monitoring data, we present our
measurements of the H$\alpha$ lags of 6 high-luminosity AGNs. Combined with the
measurements for 42 AGNs from the literature, we derive the size-luminosity
relations of H$\alpha$ BLR against broad H$\alpha$ and 5100\angstrom{}
continuum luminosities. We find the slope of the relations to be $0.61\pm0.04$
and $0.59\pm0.04$, respectively, which are consistent with the \hb{}
size-luminosity relation. Moreover, we find a linear relation between the
5100\angstrom{} continuum luminosity and the broad H$\alpha$ luminosity across
7 orders of magnitude. Using these results, we propose a new virial mass
estimator based on the H$\alpha$ broad emission line, finding that the previous
mass estimates based on the scaling relations in the literature are
overestimated by up to 0.7 dex at masses lower than $10^7$~M$_{\odot}$.
