  The mean density of a star transited by a planet, brown dwarf or low mass
star can be accurately measured from its light curve. This measurement can be
combined with other observations to estimate its mass and age by comparison
with stellar models. Our aim is to calculate the posterior probability
distributions for the mass and age of a star given its density, effective
temperature, metallicity and luminosity. We computed a large grid of stellar
models that densely sample the appropriate mass and metallicity range. The
posterior probability distributions are calculated using a Markov-chain
Monte-Carlo method. The method has been validated by comparison to the results
of other stellar models and by applying the method to stars in eclipsing binary
systems with accurately measured masses and radii. We have explored the
sensitivity of our results to the assumed values of the mixing-length
parameter, $\alpha_{\rm MLT}$, and initial helium mass fraction, Y. For a star
with a mass of 0.9 solar masses and an age of 4 Gyr our method recovers the
mass of the star with a precision of 2% and the age to within 25% based on the
density, effective temperature and metallicity predicted by a range of
different stellar models. The masses of stars in eclipsing binaries are
recovered to within the calculated uncertainties (typically 5%) in about 90% of
cases. There is a tendency for the masses to be underestimated by about 0.1
solar masses for some stars with rotation periods P$_{\rm rot}< 7$d. Our method
makes it straightforward to determine accurately the joint posterior
probability distribution for the mass and age of a star eclipsed by a planet or
other dark body based on its observed properties and a state-of-the art set of
stellar models.
