How long could humans survive only on other humans?

A tragic event strikes the Earth, killing all living plants and animals except humans. With no other food source, humans turn to cannibalism. Assuming fresh water and oxygen is still available, how long could the human species survive eating only other humans?

I imagine two possible scenarios:

1. The amount of nutrition available is finite. Eventually, only two very weak humans will be left, one eating the other.
2. The overall population will reach an equilibrium, which may fluctuate up and down, but will remain stable.
• what-if.xkcd.com/105 Mar 3, 2019 at 3:40
• Disease from rotting corpses would kill off most of the population before this became an issue Mar 3, 2019 at 12:37

Assuming the human body contains around 110,000 calories and will around 2 months, then the human population will halve every two months as one person has to die for another to survive. The population will experience exponential decay with a half-life of two months, so after a year, 1.5% of the population is left. This will continue until all humans are dead.

Unless, the humans are smart about it and proactively kill and freeze people. For example, 14% (~1/7) of the population could kill and freeze the remaining 86% (~6/7), who would contain enough nutrients to keep the 14% alive for the year, which is much more efficient than the first method. Still, all humans would die eventually, but the more people you kill at the beginning, the longer the rest will last.

The best solution would be to use renewable energy to create more food, and therefore survive indefinitely, but we don't have a way to do that effectively. Maybe, this is in the future and we can reconstitute food from our waste with energy input from the sun/environment, and in that case humans could live in a relatively small equilibrium.

• "Maybe, this is in the future and we can reconstitute food from our waste with energy input from the sun/environment" You just described farming edible plants, so not so very far in the future perhaps :) just a pity the OP's criteria involves the magical removal of all living plants, presumably including all viable seeds. Mar 3, 2019 at 2:05
• Hmm, unfortunately all non-human life here is gone so unless we can recreate the plants somehow I don’t know how the farming would work exactly. Mar 3, 2019 at 2:07
• ^ "presumably including all viable seeds" but maybe the Svalbard Global Seed Vault survives :) Mar 3, 2019 at 2:11
• "But the more people you kill at the beginning, the longer the rest will last" – this will be the tagline for the movie :) Mar 3, 2019 at 15:35
• @JeffThompson : Drop the "But" at the start ~ maybe contract a bit more to "the more you kill at the start, the longer you last" ~ maybe even chop out "at the start" as well ~ taglines should be short & punchy. Mar 3, 2019 at 16:28

See https://what-if.xkcd.com/105/ for everything you need. (I don’t have comment permission, sorry for the short answer.)

• This XKCD post is great! But jamesqf's answer covers mostly the same info (though in less detail) so I'm going to accept that one since it's not just a link. Mar 3, 2019 at 15:30

Obviously, scenario #1 is the only possible one, simply from conservation of energy. (Though the last survivors would likely be the strongest and/or sneakiest.)

Just as a rough estimate, the average human might dress out at 100 lbs of useable meat, and a human might survive on one pound of meat per day. Thus the population would be reduced by half in 100* days. So ballpark 3200 days to reduce the population to 2 individuals. Assuming the survivors can all get together and hunt each other: in actuality you'd have local & continental pockets wiping themselves out a bit sooner.

*Per other answers, 100 days is erring on the side of optimism, but the principle is the same. Exponential decay to one survivor, who then starves.

• The more I think about it, the more I think this is probably right. It would be a pretty crazy 8 years though! Mar 3, 2019 at 15:31