Context. Knowing how the mass loss of carbon-rich AGB stars depends on stellar parameters is crucial for stellar evolution modelling, as well as for the understanding of when and how circumstellar structures emerge around these stars, e.g., dust shells and so-called detached shells of expelled gas. Aims. The purpose of this paper is to explore the stellar parameter space using a numerical radiation hydrodynamic (RHD) model of carbon-star atmospheres, including a detailed description of dust formation and frequency-dependent radiative transfer, in order to determine how the mass loss of carbon stars changes with stellar parameters. Methods. We have computed a grid of 900 numeric dynamic model atmospheres (DMAs) using a well-tested computer code. This grid of models covers most of the expected combinations of stellar parameters, which are made up of the stellar temperature, the stellar luminosity, the stellar mass, the abundance of condensible carbon, and the velocity amplitude of the pulsation. Results. The resultant mass-loss rates and wind speeds are clearly affected by the choice of stellar temperature, mass, luminosity and the abundance of available carbon. In certain parts of the parameter space there is also an inevitable mass-loss threshold, below which a dust-driven wind is not possible. Contrary to some previous studies, we find a strong dependence on the abundance of free carbon, which turns out to be a critical parameter. Furthermore, we have found that the dust grains that form in the atmosphere may grow too large for the commonly used small particle approximation of the dust opacity to be strictly valid. This may have some bearing on the wind properties, although further study of this problem is needed before quantitative conclusions can be drawn. Conclusions. The wind properties show relatively simple dependences on stellar parameters above the mass-loss threshold, while the threshold itself is of a more complicated nature. Hence, we chose not to derive any simplistic mass-loss formula, but rather provide a mass-loss prescription in the form of an easy-to-use FORTRAN routine (available at http://coolstars.astro.uu.se). Since this mass-loss routine is based on data coming from an essentially self-consistent model of mass loss, it may therefore serve as a better mass-loss prescription for stellar evolution calculations than empirical formulae. Furthermore, we conclude that there are still some issues that need to be investigated, such as the rôle of grain-sizes.