Carrying capacity is a fundamental concept in rangeland science and management; however, it is difficult to define, not least because it can be viewed from varied perspectives. With a view to facilitating debate, six perspectives (or definitions) of carrying capacity were formulated, representing: resource productivity; animal production; the system; animal welfare; the environment; and profit. To explore their implications semiquantitatively, Noy-Meir's simple, two-function model of a grazing system was used to simulate the annual herbage production cycle, during which a specified animal population density would be present year-round, except during an early-season grazing deferment of specified duration. The model was extended to calculate a metric for each definition of carrying capacity and then implemented for various combinations of the two key grazing-management-determined parameters: animal density and deferment duration. The metrics were mapped as a series of response surfaces. In general, grazing deferment at the start of the growth season can compensate for an increase in animal density. In other words, carrying capacity is, for most definitions, a contour line on a response surface; it divides the total space into “acceptable” and “unacceptable” regions of grazing-management practice. The contour lines that characterize the various carrying-capacity definitions can then be superimposed to examine the degree of overlap between “acceptable” regions. Two common rules-of-thumb for determining carrying capacity are examined by using this approach. The term “carrying capacity” is vague because it can address various concerns, but some of the most important concerns can be defined in reasonably precise terms and translated into quantitative metrics, based on the fundamental states and rates of a grazing system. Such an approach could facilitate dialogue among those concerned with the continuous refinement of carrying-capacity recommendations. © 2019 The Author