  {\it Ab initio} potential energy and dipole moment surfaces are computed for
sulfur trioxide (SO$_3$) at the CCSD(T)-F12b level of theory and appropriate
triple-zeta basis sets. These surfaces are fitted and used, with a slight
correction for the equilibrium S--O distance, to compute pure rotational and
rotation-vibraton spectra of \sothree\ using the variational nuclear motion
program TROVE. The calculations considered transitions in the region 0--4000
\cm\ with rotational states up to J=85. The resulting line list of 349~348~513
transitions is appropriate for modelling room temperature SO3 spectra. Good
agreement is found with the observed infrared absorption spectra and the
calculations are used to place the measured relative intensities on an absolute
scale. A list of 10~878 experimental transitions is provided in a form suitable
for inclusion in standard atmospheric and planetary spectroscopic databases.
