The mechanisms, extent, and rate of K-storage in graphenic and graphitic carbons, as direct comparisons with Li-storage in the same structures/materials, in terms of the effects of dimensional scale and presence of surface and exposed edge sites have been brought to the fore via DFT-based simulations, duly complemented and supplemented by experimental studies. The simulation indicates feasibilities toward K-storage on single-layer graphene (SLG) at a concentration greater than that in graphite (i.e., beyond KC8), the formation of more than one layer of K on SLG, and K-storage on both the surfaces of SLG, unlike that for Li-storage. Simulations done with graphene nanoribbons (GNRs) indicate that K can get hosted on the graphene surfaces and at the exposed "stepped" edges, in addition to the "classical" K-intercalation in-between the constituent graphene layers. Accordingly, the computation studies indicate considerably enhanced K-storage "specific capacity" of GNR, as compared to bulk graphite, with the capacity decreasing with the increase in number of graphene layers. Electrochemical potassiation/depotassiation of well-ordered fairly pristine few layers graphene films (FLG; ∼6-7 layers) confirms the simultaneous occurrences of bulk (i.e., K-intercalation) and surface storage of K, resulting in reversible K-storage capacity being greater than that of thicker bulk graphite films by a factor of ∼2.5. This is in agreement with the predictions from DFT. However, this increment is less compared to that for Li-storage, again in accordance with the DFT results. Our measurements indicate lower diffusivity of K, as compared to Li, in the same graphitic structure by an order of magnitude. Accordingly, the rate capability of K-storage in graphite has been found to be considerably inferior to Li-storage, which renders the reduction in dimensional scale even more important in the case of K-storage, as observed here with FLG. © 2019 American Chemical Society.