A recently devised new method for numerical Abel inversion is compared with four other commonly used methods. One of them, the convolution method, is employed in computer tomography for reconstructing asymmetrical objects. It is investigated whether this method can be adapted for the case of radial symmetry. As a first approach the comparison is performed by computer simulation. Special attention is given to the propagation of errors according to their origin. The result is a recipe for minimizing errors and for choosing the optimal method for reconstruction. The second step is a comparison of experimentally obtained radial profiles with functions resulting from Abel inversion of measured side-on data. Thus it is shown that the concept developed by computer simulation can be applied in practice