Even though poverty indices with axiomatically sound properties have been advocated for several decades, most empirical studies of poverty in Australia and elsewhere continue to use the crude, but easily understood, head-count ratio. The difficulty of interpreting the axiomatically more desirable indices is a major reason why their use has been resisted in applied poverty measurement. This paper demonstrates how the more sophisticated poverty indices can be converted into a form that is readily interpreted as a measure of poverty intensity of a group, relative to the population to which the group belongs. The resulting poverty-intensity index is easy to understand and it retains the axiomatic properties of the poverty index on which it is based. We apply the method to Australian data. Poverty measures reported previously in the literature are converted into measures of poverty intensity and interpreted accordingly. We also calculate and interpret some new measures of poverty and poverty intensity using the 1996–97 Income and Housing Costs Survey, Australia (Australian Bureau of Statistics 1997). It is hoped our procedure will lead to wider use of poverty indices that are theoretically superior to the head-count ratio.