  The empirical relations between rotation period, chromospheric activity, and
age can be used to estimate stellar age. To calibrate these relations, we
present a catalog, including the masses and ages of 52,321 FGK dwarfs, 47,489
chromospheric activity index $logR^{+}_{HK}$, 6,077 rotation period $P_{rot}$
and variability amplitude $S_{ph}$, based on data from LAMOST DR7, Kepler and
Gaia DR3. We find a pronounced correlation among $P_{rot}$, age, and [Fe/H]
throughout the main-sequence phase for F dwarfs. However, the decrease of
$logR^{+}_{HK}$ over time is not significant except for those with [Fe/H] $<$
$-$0.1. For G dwarfs, both $P_{rot}$ and $logR^{+}_{HK}$ are reliable age
probes in the ranges $\sim$ 2-11 Gyr and $\sim$ 2-13 Gyr, respectively. K
dwarfs exhibit a prominent decrease in $logR^{+}_{HK}$ within the age range of
$\sim$ 3-13 Gyr when the relation of $P_{rot}-\tau$ is invalid. These relations
are very important for promptly estimating the age of a vast number of stars,
thus serving as a powerful tool in advancing the fields of exoplanet
properties, stellar evolution, and Galactic-archaeology.
