In recent years, cryogenic electron microscopy (Cryo-EM) has revolutionized the structure determination of wet samples and especially that of biological macromolecules. The glassy-water medium in which the molecules are embedded is considered an almost in vivo environment for biological samples. The local structure of amorphous ice is known from neutron- and X-ray-diffraction studies, techniques appropriate for much larger volumes than those used in cryo-EM. We here present a first study of the pair-distribution function g(r) of glassy water under cryo-EM conditions using electron diffraction data. We found g(r) to be between that of low-density amorphous ice and that of supercooled water. Under electron exposure, cubic-ice regions were found to nucleate in thicker glassy-water samples. Our work enables to obtain quantitative structural information using g(r) from cryo-EM.