  We present a new age-dating technique that combines gyrochronology with
isochrone fitting to infer ages for FGKM main-sequence and subgiant field
stars. Gyrochronology and isochrone fitting are each capable of providing
relatively precise ages for field stars in certain areas of the
Hertzsprung-Russell diagram: gyrochronology works optimally for cool
main-sequence stars, and isochrone fitting can provide precise ages for stars
near the main-sequence turnoff. Combined, these two age-dating techniques can
provide precise and accurate ages for a broader range of stellar masses and
evolutionary stages than either method used in isolation. We demonstrate that
the position of a star on the Hertzsprung- Russell or color-magnitude diagram
can be combined with its rotation period to infer a precise age via both
isochrone fitting and gyrochronology simultaneously. We show that incorporating
rotation periods with 5% uncertainties into stellar evolution models improves
age precision for FGK stars on the main sequence, and can, on average, provide
age estimates up to three times more precise than isochrone fitting alone. In
addition, we provide a new gyrochronology relation, calibrated to the Praesepe
cluster and the Sun, that includes a variance model to capture the rotational
behavior of stars whose rotation periods do not lengthen with the square-root
of time, and parts of the Hertzsprung-Russell diagram where gyrochronology has
not been calibrated. This publication is accompanied by an open source Python
package, stardate, for inferring the ages of main-sequence and subgiant FGKM
stars from rotation periods, spectroscopic parameters and/or apparent
magnitudes and parallaxes.
