### Abstract

Mean-field theory has been proven to be a useful description of stellar dynamos. It provides a conceptual understanding of the induction mechanisms that lead to the generation of large-scale magnetic field in stellar interiors. Our aim is to test the validity and reliability of mean-field theory by a comparison of three-dimensional geodynamo calculations with corresponding mean-field models. Therefore, we calculated the full \(\alpha\) and \(\beta\) tensors with the help of three-dimensional MHD-simulations. The resulting mean-field coefficients are confirmed by an independent analytical calculation that is applicable under the first-order-smoothing approximation. In a second step, we used these coefficients in a mean-field model and compared the results with three-dimensional calculations. Basic characteristics of the geodynamo benchmark-model,"case1", were reproduced by our mean-field model. Applied to this example, mean-field theory is a valid approximation. The investigation to which extent the mean-field approach is correct for more complicated dynamos and which of the mean-field coefficients are most important is work in progress.