Convection is a fundamental physical process in the fluid cores of planets because 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 lengthscale, are poorly quantified in planetary cores due to their strong dependence on planetary rotation, buoyancy driving and magnetic fields, which are all difficult to model under realistic conditions. In the absence of strong magnetic fields, the core convective flows are expected to be in a regime of rapidly-rotating turbulence, which remains largely unexplored to date. Here we use a combination of numerical models designed to explore this low-viscosity regime to show that the convective lengthscale becomes independent of the viscosity and is entirely determined by the flow velocity and planetary rotation. For the Earth's core, we find that the characteristic con-vective lengthscale is approximately 30km and below this scale, motions are very weak. The 30-km cutoff scale rules out small-scale dynamo action and supports large-eddy simulations of core dynamics. Furthermore, it implies that our understanding of magnetic reversals from numerical geodynamo models does not relate to the Earth, because they require too intense flows. Our results also indicate that the liquid core of the Moon might still be in an active convective state despite the absence of a present-day dynamo.