Since the beginning of 1996, the vacuum-ultraviolet telescope and spectrograph SUMER (Solar Ultraviolet Measurements of Emitted Radiation) on the Solar and Heliospheric Observatory (SOHO) of ESA and NASA, has obtained radiance spectra of many features of the quiescent and active Sun with high spectral and spatial resolutions. Irradiance measurements of line emissions have also been performed in the wavelength range 58.4 nm to 154.8 nm. The instrument was calibrated against the electron storage ring BESSY I as a primary source standard with the help of a transfer source standard based on a hollow-cathode discharge lamp. A thorough cleanliness programme, specifically aimed at chemical contamination control, resulted in an excellent radiometric stability of the normal-incidence optical system as well as of the detectors. This was verified under operational conditions by various techniques employed during the SOHO mission, such as line-ratio studies, star observations and comparisons with other instruments. The observations provide vacuum-ultraviolet radiometry of the Sun in many emission lines of atoms and ions with a relative uncertainty of 0.15 (1 σ) for the wavelength range 54 nm to 125 nm.