Gaia DR2 published positions, parallaxes and proper motions for an unprecedented 1,331,909,727 sources, revolutionising the field of Galactic dynamics. We complement this data with the Astrometric Spread Function (ASF), the expected uncertainty in the measured positions, proper motions and parallax for a non-accelerating point source. The ASF is a Gaussian function for which we construct the 5D astrometric covariance matrix as a function of position on the sky and apparent magnitude using the Gaia DR2 scanning law and demonstrate excellent agreement with the observed data. This can be used to answer the question ‘What astrometric covariance would Gaia have published if my star was a non-accelerating point source?’. The ASF will enable characterisation of binary systems, exoplanet orbits, astrometric microlensing events and extended sources which add an excess astrometric noise to the expected astrometry uncertainty. By using the ASF to estimate the unit weight error (UWE) of Gaia DR2 sources, we demonstrate that the ASF indeed provides a direct probe of the excess source noise. We use the ASF to estimate the contribution to the selection function of the Gaia astrometric sample from a cut on astrometric_sigma5d_max showing high completeness for G < 20 dropping to < 1% in underscanned regions of the sky for G = 21. We have added an ASF module to the Python package scanninglaw(https://github. com/gaiaverse/scanninglaw) through which users can access the ASF.