Atmospheric carbon poses an existential threat to civilization via global climate change. Hundreds of gigatonnes of carbon dioxide must be removed from Earth’s atmosphere in the next three decades, necessitating a low-cost, energy-efficient process to extract low concentrations of carbon dioxide for conversion to a stable material permanently stored for thousands of years. In this work, the challenge of removing gigatonnes of CO2 is described via the scale of effort and the thermodynamics of collecting and reducing this diffuse chemical, the accumulation of which imparts a substantial entropy penalty on any atmospheric carbon capture process. The methods of CO2 reduction combined with upstream direct air capture (DAC) including absorption, membrane separation, and adsorption are compared with biomass torrefaction and permanent burial (BTB). A Monte Carlo model assesses the mass, energy, and economics of the full process of biomass torrefaction from biomass collection and transport to stable carbon burial to determine that 95% of scenarios could remove carbon for less than $200 per CO2-tonne-equivalent. Torrefied carbon is further discussed for its long-term stability and availability at the scale required to substantially mitigate the threat of climate change.