1. The maximum annual population growth rate (rm) is a critical parameter in many models of wildlife dynamics and management. An important application of rm is the estimation of the maximumproportion of a population that can be removed to stop population growth (p). 2. When rm cannot be estimated in the field, one option is to estimate it from demographic data. We evaluate the use of the relationship between rm and female age at first reproduction (a), which is independent of phylogeny, to estimate rm. We first demonstrate that the relationship between field and demographic estimates of rm is unbiased. We then show that the relationship provides an unbiased and simple method to estimate rm using data for 64 mammal species. We also show that p declines exponentially as a increases. 3. We use the fitted relationship to estimate annual rm and p for 55 mammal species in Australia and New Zealand for which there are no field estimates of rm. The estimates differ by species but have low precision (wide 95% credible intervals CIs). Our estimate of rm for the Tasmanian devil Sarcophilus harrisii is high (0Æ6, 95% CI: 0Æ05–2Æ39) and suggests devils would become extinct if >0Æ34 of the population is removed annually (e.g. by facial tumour disease). Our estimate of rm (0Æ77, 95%CI: 0Æ71–1Æ05) for brushtail possumTrichosurus vulpecula is much greater than published estimates and highlights the need for further field estimates of rm for the species in New Zealand. 4. Synthesis and applications. Since rm has not been estimated in the field for themajority ofmammal species, our approach enables estimates with credible intervals for this important parameter to be obtained for any species for which female age at first reproduction is known. However, the estimates havewide 95%CIs. The estimated rm, and associated uncertainty can then be used in population and management models, perhaps most importantly to estimate the proportion that if removed annually would drive the population to extinction.Our approach can be used for taxa other hanmammals.