An analytic sensitivity method is proposed for the transient security assessment of large power systems. It is based on the recently developed ‘extended equal area criterion’, and on a related transient stability margin. It is shown that this margin leads to a simple algebraic formulation of sensitivity coefficients. Particular attention is focused on the sensitivity with respect to generation power, and possible applications to power system planning and online operation are suggested. For example, the computation of generation and load supply limits provides transient stability constraints and thence means of online transient security assessment and preventive control. Within the limits of the simplified electromotive force behind the transient reactance model, the method proves to be accurate, demanding very little with respect to computing time and fairly independent of the system size. The simulation results reported in the paper corroborate these conclusions.