Energy-based acoustic quantities provide vital information about acoustic fields and the characterization of acoustic sources. Recently, the phase and amplitude gradient estimator (PAGE) method has been developed to reduce error and extend bandwidth of energy-based quantity estimates. To inform uses and applications of the method, analytical and experimental characterizations of the method are presented. Analytical PAGE method bias errors are compared with those of traditional estimation for two- and three-microphone one-dimensional probes. For a monopole field when phase unwrapping is possible, zero bias error is achieved for active intensity using three-microphone PAGE and for specific acoustic impedance using two-microphone PAGE. A method for higher-order estimation in reactive fields is developed, and it is shown that a higher-order traditional method outperforms higher-order PAGE for reactive intensity in a standing wave field. Extending the applications of PAGE, the unwrapped phase gradient is used to develop a method for directional sensing with improved bandwidth and arbitrary array response.