We have measured the absolute photon number of single-shot high-order harmonic spectra generated by focusing intense short pulsed laser radiation into a gas target with a calibrated extreme ultraviolet (EUV) spectrometer. For the calibration, we used a compact hollow-cathode source as a radiometric transfer standard providing radiation from rare gas plasma emission lines of known radiant intensity in the spectral range from 13.1 nm to 58.4 nm. The photon number measurement is based on the comparison of the detected signals of the high-order harmonics and the hollow-cathode emission lines with nearly identical spectrometer set-ups. This technique provides a measurement of the harmonics photon number with a relative uncertainty of less than 50% (1 σ).