| Summary: | 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 $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ , 6077 rotation periods P _rot , and variability amplitudes S _ph , based on data from LAMOST DR7, Kepler, and Gaia Data Release 3. We find a pronounced correlation among P _rot , age, and [Fe/H] throughout the main-sequence phase for F dwarfs. However, the decrease of $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ over time is not significant except for those with [Fe/H] < −0.1. For G dwarfs, both P _rot and $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ are reliable age probes in the ranges ∼2–11 Gyr and ∼2–13 Gyr, respectively. K dwarfs exhibit a prominent decrease in $\mathrm{log}{R}_{\mathrm{HK}}^{+}$ within the age range of ∼3–13 Gyr when the relation of P _rot – τ 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 archeology.
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