An experimental scheme to realize single-shot spectrometry for the diagnostics of x-ray free-electron lasers (XFELs) is presented. The combination of an ultraprecisely figured mirror and a perfect crystal form a simple, high-precision spectrometer that can cover an energy range from a few eV to a hundred eV with high resolution. The application of the spectrometer to determine XFEL pulse widths was investigated theoretically and experimentally. It has been shown that the present system can determine pulse widths from sub-fs to ps in a single shot even for spontaneous radiation. The system can be easily extended to even shorter pulses.