Abstract. From basic physical assumptions we derive a simple linear model of the global CO₂ cycle without free parameters. It yields excellent agreement with the observations reported by the carbon dioxide information analysis center (CDIAC) as time series of atmospheric CO₂ growth, of sinks in the ocean and of absorption by the biosphere. The agreement extends from the year 1850 until present (2013). Based on anthropogenic CO₂ emission scenarios until 2150, future atmospheric CO₂ concentrations are calculated. As the model shows, and depending on the emission scenario, the airborne fraction of CO₂ begins to decrease in the year ~ 2050 and becomes negative at the latest in ~ 2130. At the same time the concentration of the atmospheric CO₂ will reach a maximum between ~ 500 and ~ 900 ppm. As a consequence, increasing anthropogenic CO₂ emissions will make the ocean and the biosphere the main reservoirs of anthropogenic CO₂ in the long run. Latest in about 150 years, anthropogenic CO₂ emission will no longer increase the CO₂ content of the atmosphere.