High precision energy measurements from the analysis of wide spectral features. Application to the fluorescence of YAG:Ce3+

•The fluorescent spectrum of YAG:Ce is calculated with no adjustable parameter.•Full quantitative agreement with high resolution experimental data is attained.•Same agreement of theory and experiment at zero and room temperatures.•Theory is realistic and analytical, hence calculations are precise and rapid.•Precision of transition energies is given by the theoretical fit of lineshapes.