A radiation detecting apparatus of this invention includes an arithmetic processing device which carries out arithmetic processes for drawing boundaries based on peaks of signal strengths and separating respective positions by the boundaries, and for determining, by using spatial periodicity of the peaks, the number of peaks having failed to be separated, with a plurality of peaks connecting to each other. If the separation fails with a plurality of peaks connecting to each other, the number of peaks in error is determined using spatial periodicity of the peaks. Thus, by using spatial periodicity of the peaks, the number of peaks in error can be determined and boundaries can be set easily. As a result, incident positions can also be discriminated easily, and detecting positions of radiation can be determined easily.