This paper proposes a mathematically-rigorous metric to precisely describe how a disturbance in the power grid affects the system frequency, and thereby, theoretically evaluate the frequency performance of the system. This metric is inspired by the fact that the inertia of a single generator is in inverse proportion to the instantaneous rate of change of frequency (RoCoF) under a disturbance, e.g., a load step. Then, based on calculating the bus frequencies, the metric is rigorously proposed for multi-machine system. The validity and effectiveness of the proposed metric are illustrated via simulations on a multi-machine system.