A feasible way to avoid the risk of energy decline and combat climate change is to build a 100% renewable global energy mix. However, a globally electrified economy cannot grow much above 12 electric terawatts without putting pressure on the limits of finite mineral reserves. Here we analyze whether 12 TW of electricity and 1 TW of biomass (final) power will be able to fuel a future post-carbon economy that can provide similar services to those of a contemporary economy. Contrarily to some pessimistic expectations, this analysis shows that the principle economic processes can be replaced with sustainable alternatives based on electricity, charcoal, biogas and hydrogen. Furthermore, those services that cannot be replaced are not as crucial so as to cause a return to a pre-industrial society. Even so, land transport and aviation are at the limit of what is sustainable, outdoor work should be reorganized, metal primary production should be based on hydrogen reduction when possible, mineral production should be increasingly based on recycling, the petrochemical industry should shrink to a size of 40%–43% of the 2012 petrochemical sector, i.e., a size similar to that the sector had in 1985–1986, and agriculture may require organic farming methods to be sustainable.