When a point source radiates steadily in a rectangular enclosure and excites one mode only, its power outputWdepends strongly on its position. Distribution functions forWare found when the source is positioned randomly, and an axial, tangential, or oblique mode is excited. The functions for these three cases form a consistent family of curves, whose shapes are controlled by the mode shapes. The space‐averaged value ofW, i.e., the average for all source positions in the enclosure, does not equal the free‐field valueW0, but depends on the modal damping. The value ofW0can be derived from sound‐pressure measurements, however. The results are derived theoretically, and checked by a Monte Carlo procedure. Some experimental data which confirm the theoretical results are given for a small source driving an axial mode in a reverberation chamber. The work has application to standard methods of measuring the sound power output of a source.