Abstract Tropical peatlands store over 75 gigatons of carbon as organic matter that is protected from decomposition and fire by waterlogging if left undrained. Over millennia, this organic matter builds up between channels or rivers into gently mounded shapes called peat domes. Measurements of peat accumulation and water flow suggest that tropical peat domes approach a steady state in which the peat surface morphology is described by a uniform curvature, setting a limit on the carbon that a peatland can store. We explored the maximum amount of carbon that can accumulate as water-saturated peat in natural and artificial drainage networks of northwest and southern Borneo. We find that the maximum volume of peat accumulation in a channel-bounded parcel is proportional to the square of the parcel area times a scale-independent factor describing the shape of the parcel boundary. Thus, carbon capacity per area scales roughly with mean parcel area in the peatland. Our analysis provides a tool that can be used to predict the long-term impacts of artificial drainage, and to devise optimal strategies for arresting fires and greenhouse gas emissions in tropical peatlands.