Significant advances in development of the optical wavelength range require high-quality optical systems to create optoelectronic equipment on their basis characterized by high speed and information capacity. A method for calculating a compact-size Offner spectrometer was developed having the advantages of its compactness, maintaining high optical characteristics and having relatively low cost in comparison with the large-size equipment. The method is based on using the Rowland circles and the coma and astigmatism correction in the image plane. Analytical expressions were obtained making it possible to calculate design parameters of the spectrometer optical scheme. Two examples of calculating optical systems for visible and infrared ranges were considered. Calculated systems were simulated in the Zemax software program. To evaluate the synthesized optical models image quality, the confusion spot radius in the image plane was used. It is demonstrated that the confusion spot radius value does not exceed the value of the radiation receiver pixel size in the considered spectral ranges. Optimization was carried out for the IR spectrometer according to overall dimensions in order to improve the design manufacturability. It is shown that the principles laid down in the method development are effective, and the method itself could be used in design and development of new small-size hyperspectral optoelectronic equipment