  We conduct a systematic study on the light curves of type II supernovae (SNe
II) to investigate how they are affected by the physical properties of the
progenitor and the nature of the explosion. The calculations of pre-supernova
evolution, the launch of the explosion, and the light curve are carried out by
\texttt{MESA} and \texttt{STELLA}. Our study encompasses a wide range of
zero-age-main-sequence (ZAMS) masses (10 - 20 $M_{\rm \odot}$), wind mass-loss
rates (which control the range of hydrogen-rich envelope mass to be 3 - 12
$M_{\rm \odot}$), explosion energies (0.1 - 2.5 $\times$ 10$^{51}$ erg), and
$^{56}$Ni masses (0 - 0.15 $M_{\rm \odot}$). Our analyses reveal that when the
explosion energy is fixed, the light curve is primarily determined by the
properties of the hydrogen-rich envelope, despite the large variation in the
ZAMS masses. The dependencies of the light-curve characteristics on the
envelope mass, radius, and explosion energy are investigated, and we establish
the scaling relations connecting these quantities. We further derive a formula
that corrects for effects of the $^{56}$Ni heating based on observables. Using
the derived equations, we develop a method that can constrain the envelope mass
with uncertainty within 1 $M_{\rm \odot}$ based on photometry. This method is
applied to a large sample of $\sim$ 100 SNe II, which reveals a considerably
broader range of the envelope masses estimated from observables as compared to
those predicted by single star models evolving with standard stellar wind; this
finding indicates that a large fraction of SNe II experience substantial
mass-loss beyond the standard mass-loss prescription prior to their explosions,
highlighting the uncertainties involved in the massive star evolution and
pre-SN mass-loss mechanism.
