Current lipidomics approaches require simple and rapid algorithms enabling the interpretation of mass spectra of lipids. Most lipids are complex mixtures of related components in which the composition of the aliphatic fatty acid chains varies from one molecule to the next. Triacylglycerols (TAGs) are an example of such a lipid class. Fatty acid chains are the only parts of the molecule to change from one species to another. Fatty acids, and consequently also TAGs, can be characterized by two parameters; the number of carbon atoms and the number of double bonds. All calculations reflecting relations among ions in the spectra can be easily made using these parameters. An algorithm for the automated interpretation of TAGs from atmospheric pressure chemical ionization mass spectra (TriglyAPCI) is presented in this paper. The algorithm first identifies diacylglycerol fragments and molecular adducts. In the next step, relations among the ions are searched and possible TAG structures are suggested. Individual features of the algorithm are described in detail and the software performance is demonstrated for the liquid chromatography/mass spectrometric (LC/MS) analysis of TAGs isolated from the termite Prorhinotermes canalifrons.