Species abundance distributions (SADs) are widely used as a tool for summarizing ecological communities but may have different shapes, depending on the currency used to measure species importance. We develop a simple plotting method that links SADs in the alternative currencies of numerical abundance and biomass and is underpinned by testable predictions about how organisms occupy physical space. When log numerical abundance is plotted against log biomass, the species lie within an approximately triangular region. Simple energetic and sampling constraints explain the triangular form. The dispersion of species within this triangle is the key to understanding why SADs of numerical abundance and biomass can differ. Given regular or random species dispersion, we can predict the shape of the SAD for both currencies under a variety of sampling regimes. We argue that this dispersion pattern will lie between regular and random for the following reasons. First, regular dispersion patterns will result if communities are comprised groups of organisms that use different components of the physical space (e.g. open water, the sea bed surface or rock crevices in a marine fish assemblage), and if the abundance of species in each of these spatial guilds is linked to the way individuals of varying size use the habitat. Second, temporal variation in abundance and sampling error will tend to randomize this regular pattern. Data from two intensively studied marine ecosystems offer empirical support for these predictions. Our approach also has application in environmental monitoring and the recognition of anthropogenic disturbance, which may change the shape of the triangular region by, for example, the loss of large body size top predators that occur at low abundance.