For late-type non-active stars, gravitational redshifts and convective blueshifts are the main source of biases in the determination of radial velocities. If ignored, these effects can introduce systematic errors of the order of ˜ 0.5 km s-1. We demonstrate that three-dimensional hydrodynamical simulations of solar surface convection can be used to predict the convective blue-shifts of weak spectral lines in solar-like stars to ˜ 0.070 km s-1. Using accurate trigonometric parallaxes and stellar evolution models, the gravitational redshifts can be constrained with a similar uncertainty, leading to absolute radial velocities accurate to ˜ 0.1 km s-1.