An analysis of the burn equilibria of fusion reactors of the tokamak family is presented. The global (zero-dimensional) analysis is self-consistent in that it takes into account the dependence of the energy confinement on the variables of the burning plasma, such as temperature and density. Universal burn contours are presented for a selection of commonly used scaling laws for energy confinement. It is shown that the output power of a fusion reactor is to good approximation inversely proportional to the particle confinement time, due to the choking effect of the accumulation of helium, the ash of the fusion reaction. It is further shown that, whereas a fusion reactor requires a minimum energy confinement time to ignite, the output power reaches a maximum for an energy confinement that lies about 30% above this minimum. Further improvement of confinement will lower the output, although in some cases the ß limit will be the limiting factor. Given that for maximum performance density the confinement and fuel mix are best chosen to be optimal, the particle confinement is proposed as an attractive parameter for burn control.