  This paper revisits the problem of the string decay contribution to the axion
cosmological energy density. We show that this contribution is proportional to
the average relative increase when axion strings decay of a certain quantity
$N_{\rm ax}$ which we define. We carry out numerical simulations of the
evolution and decay of circular and non-circular string loops, of bent strings
with ends held fixed, and of vortex-antivortex pairs in two dimensions. In the
case of string loops and of vortex-antivortex pairs, $N_{\rm ax}$ decreases by
approximately 20%. In the case of bent strings, $N_{\rm ax}$ remains constant
or increases slightly. Our results imply that the string decay contribution to
the axion energy density is of the same order of magnitude as the
well-understood contribution from vacuum realignment.
