Transport electrification and grid storage hinge largely on fast-charging capabilities of Li- and Na-ion batteries, but anodes such as graphite with plating issues drive the scientific focus towards anodes with slopped storage potentials. Here we report fast charging of ampere-hour-level full Na-ion batteries within about 9 minutes for continuous 3,000 cycles based on hard carbon anodes. These anodes, in addition to displaying a sloped storage voltage, provide capacity at a nearly constant voltage just above the plating potential, without observing Na-metal plating under high areal capacity. Comparing the electrochemical behaviour of Li and Na in hard carbon through experimental and computational techniques, a unified storage mechanism relying on the dimensions of wedge nanopores and drawing parallels with underpotential deposition for metals is brought forward, providing a rational guide for achieving fast storage in hard carbon anodes.