A study of fusion-barrier distributions through an analysis of their moments is presented. The moments can be obtained from least-squares fits of the energy-weighted fusion cross sections without the need of calculating second derivatives. The zeroth and first moments determine the fusion radius $R$ and the Coulomb barrier ${V}_{C}$. These two quantities are the same as the parameters $R$ and ${V}_{C}$ that are used in the well-known expression, $E\ensuremath{\sigma}=\ensuremath{\pi}{R}^{2}(E\ensuremath{-}{V}_{C})$, for the fusion cross section at high energies. The second and third moments, ${M}_{2}$ and ${M}_{3}$, determine the width and skewness of the barrier distribution, respectively. From these global parameters new correlations for the study of heavy-ion-induced fusion reactions can be obtained. Systems exhibiting a large coupling to transfer reactions show a small fusion radius as well as a large second moment. A negative third moment is correlated with a prolate deformation of the target nucleus.