Seismic instruments record horizontal ground motion into two orthogonal components, and the orientations of the components are dependent on the installed sensors. Ground‐motion measures directly derived from the two components vary with the installation orientation, which will influence the result of the seismic design of structures and the variance of ground‐motion prediction equations. Various orientation‐independent measures have been proposed recently. We provide a thorough analysis of these measures and propose a new fast approach to compute most of them. The approach is based on the projected envelope algorithm that generates the omni‐spectrum of horizontal ground motion, and its computation speed is faster than previous methods for this purpose. Visualizing the omni‐spectrum helps to identify the maximum demand orientation and to capture effects of directionality. Moreover, most previous orientation‐independent measures can be represented concisely in the functional form of the omni‐spectrum.