The ecological impact of alien species is a function of the area colonised. Impact assessments of alien species are thus incomplete unless they take the spatial component of invasion processes into account. This paper describes a measure, termed expansion speed, that quantifies the speed with which a species increases its spatial presence in an assessment area. It is based on the area of occupancy (AOO) and can be estimated from grid occupancies. Expansion speed is defined as the yearly increase in the radius of a coherent circle having the same area as the AOO, irrespective of whether the increase is due to natural dispersal or anthropogenic transport. Two methods for estimating expansion speed are presented: one that requires several years of spatio-temporal observation data and explicitly takes detection rates into account; and one that can be used under a situation with sparse data. Using simulations and real-world data from natural history collections, it is shown that the method provides a good fit to observational datasets. Expansion speed has several valuable properties. Being based on AOO, it is an intuitive measure; as it only requires occupancy data, it is comparatively easy to estimate; and because it is a quantitative and generic measure, it increases the testability and comparability of impact assessments of alien species.