  The calculation of distances is of fundamental importance in extragalactic
astronomy and cosmology. However, no practical implementation for the general
case has previously been available. We derive a second-order differential
equation for the angular size distance valid not only in all em homogeneous
Friedmann-Lemaitre cosmological models, parametrised by $\lambda_{0}$ and
$\Omega_{0}$, but also in inhomogeneous `on-average' Friedmann-Lemaitre models,
where the inhomogeneity is given by the (in the general case
redshift-dependent) parameter $\eta$. Since most other cosmological distances
can be obtained trivially from the angular size distance, and since the
differential equation can be efficiently solved numerically, this offers for
the first time a practical method for calculating distances in a large class of
cosmological models. We also briefly discuss our numerical implementation,
which is publicly available.
