The kinetics of island nucleation and growth during deposition of Cu atoms on Cu(001) is studied using rate equations. The equations are derived using microscopic calculations of the energy landscape on the surface, previously used in Monte Carl (MC) simulations. This allows a quantitative comparison between the rate equations and the MC results. Our rate equations take into account atoms that fall on the bare substrate as well as on top of existing islands, the mobility of single atoms and small islands, the coalescence of adjacent islands and the possible separation of atoms from island edges. The rate equations are used to explore the island size distribution and island density as a function of the coverage and deposition rates. These rate equations provide a useful and flexible tool that allows to easily modify particular microscopic properties of the system such as the mobility of small islands or the rate of coalescence and examine their effect while leaving all other features intact.