  The rotation-mass-age relationship offers a promising avenue for measuring
the ages of field stars, assuming the attendant uncertainties to this technique
can be well characterized. We model stellar angular momentum evolution starting
with a rotation distribution from open cluster M37. Our predicted
rotation-mass-age relationship shows significant zero-point offsets compared to
an alternative angular momentum loss law and published gyrochronology
relations. Systematic errors at the 30 percent level are permitted by current
data, highlighting the need for empirical guidance. We identify two fundamental
sources of uncertainty that limit the precision of rotation-based ages and
quantify their impact. Stars are born with a range of rotation rates, which
leads to an age range at fixed rotation period. We find that the inherent
ambiguity from the initial conditions is important for all young stars, and
remains large for old stars below 0.6 solar masses. Latitudinal surface
differential rotation also introduces a minimum uncertainty into rotation
period measurements and, by extension, rotation-based ages. Both models and the
data from binary star systems 61 Cyg and alpha Cen demonstrate that latitudinal
differential rotation is the limiting factor for rotation-based age precision
among old field stars, inducing uncertainties at the ~2 Gyr level. We also
examine the relationship between variability amplitude, rotation period, and
age. Existing ground-based surveys can detect field populations with ages as
old as 1-2 Gyr, while space missions can detect stars as old as the Galactic
disk. In comparison with other techniques for measuring the ages of lower main
sequence stars, including geometric parallax and asteroseismology,
rotation-based ages have the potential to be the most precise chronometer for
0.6-1.0 solar mass stars.
