In recent years there has been much interest concerning the development of modulators in the mid- to long-wave infrared, based on emerging materials such as graphene. These have been frequently pursued for optical communications, though also for other specialized applications such as infrared scene projectors. Here we investigate a new application for graphene modulators in the mid- to long-wave infrared. We demonstrate, for the first time, computational spectroscopy in the mid- to long-wave infrared using a graphene-based metasurface modulator. Furthermore, our metasurface device operates at low gate voltage. To demonstrate computational spectroscopy, we provide our algorithm with the measured reflection spectra of the modulator at different gate voltages. We also provide it with the measured reflected light power as a function of the gate voltage. The algorithm then estimates the input spectrum. We show that the reconstructed spectrum is in good agreement with that measured directly by a Fourier transform infrared spectrometer, with a normalized mean-absolute-error (NMAE) of 0.021.