The chemical changes and absolute rates in radiation damage to polyethylene terephthalate (PET) caused by soft X-rays and energetic electrons have been measured using a scanning transmission X-ray microscope (STXM). Electron beam damage at two different dose rates and a range of doses was performed in an 80 keV transmission electron microscope (TEM). The STXM beam was used to create damage patterns with systematically varied doses of monochromatic soft X-rays on an adjacent piece of the same PET sample. NEXAFS spectroscopy at the C 1s and O is edges was used to study the chemistry of the radiation damage and to determine quantitative critical doses for PET damage by both types of radiation. The spectral changes were similar for damage by electrons and X-rays, indicating the radiation chemistry is dominated by secondary processes, not the primary event. The critical dose for chemical changes determined from C 1s spectral features is 4.2(6) x 10(8) Gy and was the same for soft X-rays and electrons within measurement uncertainties. The critical dose for specific damage processes (as defined by changes in several different, bond-specific spectral features) was found to be similar in the C 1s region and was comparable between C 1s and O Is edges for electron beam damage. There were statistically different critical doses for soft X-ray damage as probed by changes in O 1s spectral features related to carbonyl and ester bonds.