We present the calibration of the Swift Ultraviolet and Optical Telescope (UVOT ) grisms, of which there are two, providing low-resolution field spectroscopy in the ultraviolet and optical bands, respectively. The UV grism covers the range λ1700–5000 Å with a spectral resolution (λ/Δλ) of 75 at λ2600 Å for source magnitudes of u=10–16 mag, while the visible grism covers the range λ2850–6600 Å with a spectral resolution of 100 at λ4000 Å for source magnitudes of b=12–17 mag. This calibration extends over all detector positions, for all modes used during operations. The wavelength accuracy (1σ) is 9 Å in the UV grism clocked mode, 17 Å in the UV grism nominal mode and 22 Å in the visible grism. The range below λ2740 Å in the UV grism and λ5200 Å in the visible grism never suffers from overlapping by higher spectral orders. The flux calibration of the grisms includes a correction we developed for coincidence loss in the detector. The error in the coincidence loss correction is less than 20 per cent. The position of the spectrum on the detector only affects the effective area (sensitivity) by a few per cent in the nominal modes, but varies substantially in the clocked modes. The error in the effective area is from 9 per cent in the UV grism clocked mode to 15 per cent in the visible grism clocked mode.