  (abridged) We present a new tool for building synthetic colour-magnitude
diagrams of coeval stellar populations. We study, from a theoretical point of
view, the impact of axial rotation of stars on various observed properties of
single-aged stellar populations: magnitude at the turnoff, photometric
properties of evolved stars, surface velocities, surface abundances, and the
impact of rotation on the age determination of clusters by an isochrone
fitting. Stellar models for different initial masses, metallicities, and
zero-age main sequence (ZAMS) rotational velocities are used for building
interpolated stellar tracks, isochrones, and synthetic clusters for various
ages and metallicities. The synthetic populations account for the effects of
the initial distribution of the rotational velocities on the ZAMS, the impact
of the inclination angle and the effects of gravity and limb darkening,
unresolved binaries and photometric errors. Interpolated tracks, isochrones,
and synthetic clusters can be computed through a public web interface. For
clusters with a metallicity in the range [0.002, 0.014] and an age between 30
Myr and 1 Gyr, the fraction of fast rotators on the main sequence (MS) band is
the largest just below the turnoff. This is a natural consequence of the
increase in the MS lifetime due to rotation. The fraction of fast rotators one
magnitude below the turnoff also increases with the age of the cluster between
30 Myr and 1 Gyr. There is an increase in the fraction of enriched stars when
the metallicity decreases. We show that the use of isochrones computed from
rotating stellar models with an initial rotation that is representative of the
average initial rotation of the stars in clusters provides a reasonable
estimate of the age, even though stars in a real cluster did not start their
evolution with an identical initial rotation.
