  The stiffness of the hadronic equation of state has been extracted from the
production rate of $K^+$ mesons in heavy ion collisions around 1 $A$ GeV
incident energy. The data are best described with a compressibility coefficient
$\kappa$ around 200 MeV, a value which is usually called ``soft''. This is
concluded from a detailed comparison of the results of transport theories with
the experimental data using two different procedures: (i) the energy dependence
of the ratio of $K^+$ from Au+Au and C+C collisions and (ii) the centrality
dependence of the $K^+$ multiplicities. It is demonstrated that input
quantities of these transport theories which are not precisely known, like the
kaon-nucleon potential, the $\Delta N \to N K^+ \Lambda$ cross section or the
life time of the $\Delta$ in matter do not modify this conclusion.
