An ionization chamber with a Frisch grid is used to determine both the energy (E) of the charged particles emitted from the source positioned coplanar with the cathode, and the cosine of the emission angle (ϑ) with respect to the normal of the cathode. In the plane determined by the variables cosϑ and E, it is possible to identify an area that is unaffected by backscattering and self-absorption. Events belonging to this area show an isotropic angular distribution for alpha particles and also for fragments of fission induced by thermal neutrons, which, extrapolated to 90 deg, yields the absolute number of events. The capabilities of this technique are demonstrated by the investigation of four evaporated 235UF4 layers and one suspension-sprayed 235U3O8 layer. For the UF4 layers, the alpha-particle source strengths were determined, and agreement was found within 0.3% with values independently measured by low-geometry alpha counting. The same method was also applied to fission events induced by thermal neutrons. The determination of the total number of fission events is determined to an accuracy of better than 0.5%. The longstanding doubts on the magnitudes of fragment absorption and scattering are, in principle, circumvented by the present method, and therefore no assumptions on fragment ranges and scattering cross sections are needed. It is emphasized that the present method, within reasonable limits, is insensitive to source shape and homogeneity in its thickness.