The present-day abundance of beryllium in the solar atmosphere provides clues about mixing mechanisms within stellar interiors. However, abundance determinations based on the BeII 313.107nm line are prone to systematic errors due to imperfect model spectra. These errors arise from missing continuous opacity in the UV, a significant unidentified blend at 313.102nm, departures from local thermodynamic equilibrium (LTE), and microturbulence and macroturbulence fudge parameters associated with one-dimensional (1D) hydrostatic model atmospheres. Although these factors have been discussed in the literature, no study has yet accounted for all of them simultaneously. To address this, we present 3D non-LTE calculations for neutral and ionised beryllium in the Sun. We used these models to derive the present-day solar beryllium abundance, calibrating the missing opacity on high resolution solar irradiance data and the unidentified blend on the centre-to-limb variation. We find a surface abundance of 1.21+/-0.05dex, which is significantly lower than the value of 1.38dex that has been commonly adopted since 2004. Taking the protosolar beryllium abundance via CI chondrites, 1.32+/-0.04dex, our result implies that the surface abundance of beryllium has been depleted by 0.11+/-0.06dex, or 22+/-11%. This is in tension with standard solar models, which predict negligible depletion, as well as with contemporary solar models that have extra mixing calibrated on the abundances of helium and lithium, which predict excessive depletion. These discrepancies highlight the need for further improvements to the physics in solar and stellar models.