  As part of a larger program aimed at better quantifying the uncertainties in
stellar computations, we attempt to calibrate the extent of convective
overshooting in low to intermediate mass stars by means of eclipsing binary
systems. We model 12 such systems, with component masses between 1.3 and 6.2
solar masses, using the detailed binary stellar evolution code STARS, producing
grids of models in both metallicity and overshooting parameter. From these, we
determine the best fit parameters for each of our systems. For three systems,
none of our models produce a satisfactory fit. For the remaining systems, no
single value for the convective overshooting parameter fits all the systems,
but most of our systems can be well described with an overshooting parameter
between 0.09 and 0.15, corresponding to an extension of the mixed region above
the core of about 0.1-0.3 pressure scale heights. Of the nine systems where we
are able to obtain a good fit, seven can be reasonably well fit with a single
parameter of 0.15. We find no evidence for a trend of the extent of
overshooting with either mass or metallicity, though the data set is of limited
size. We repeat our calculations with a second evolution code, MESA, and we
find general agreement between the two codes. For the extension of the mixed
region above the convective core required by the MESA models is about 0.15-0.4
pressure scale heights. For the system EI Cep, we find that MESA gives an
overshooting region that is larger than the STARS one by about 0.1 pressure
scale heights for the primary, while for the secondary the difference is only
0.05 pressure scale heights.
