Convection is a fundamental physical process in the fluid cores of planets. It is the primary transport mechanism for heat and chemical species and the primary energy source for planetary magnetic fields. Key properties of convection-such as the characteristic flow velocity and length scale-are poorly quantified in planetary cores owing to the strong dependence of these properties on planetary rotation, buoyancy driving and magnetic fields, all of which are difficult to model using realistic conditions. In the absence of strong magnetic fields, the convective flows of the core are expected to be in a regime of rapidly rotating turbulence(1), which remains largely unexplored. Here we use a combination of non-magnetic numerical models designed to explore this regime to show that the convective length scale becomes independent of the viscosity when realistic parameter values are approached and is entirely determined by the flow velocity and the planetary rotation. The velocity decreases very rapidly at smaller scales, so this turbulent convective length scale is a lower limit for the energy-carrying length scales in the flow. Using this approach, we can model realistically the dynamics of small non-magnetic cores such as the Moon. Although modelling the conditions of larger planetary cores remains out of reach, the fact that the turbulent convective length scale is independent of the viscosity allows a reliable extrapolation to these objects. For the Earth's core conditions, we find that the turbulent convective length scale in the absence of magnetic fields would be about 30 kilometres, which is orders of magnitude larger than the ten-metre viscous length scale. The need to resolve the numerically inaccessible viscous scale could therefore be relaxed in future more realistic geodynamo simulations, at least in weakly magnetized regions.