The UN has reported that all factors being equal (which to my way of thinking assumes enough food, no super-viruses, no meteor impacts, and no sudden runaway global warming Extinction Level Events), the population by 2100 should be something like:
By the end of the century, the world’s population will be roughly: one billion in Europe, one billion in the Americas, four billion in Africa, five billion in Asia.
But as Breakthrough author Alex Trembath says in his email circular,
But there’s reason to think global population will never reach 10 billion, let alone 11. Most of the increase in population is projected to occur in Africa, where most countries still have not undergone their own demographic transition. But according to Samir K C at IIASA, the total population of African countries might not grow to 4.4 billion (from around 1 billion today) like the United Nations suggests:
According to our projections at the Wittgenstein Center, projecting population by age, sex, and educational attainment for almost all countries of the World, Africa’s population may only rise to some 2.6 billion by 2100. That number is only 60% of the 4.4 billion predicted by the UN.
The size of the global population is a critical variable in determining what point this century we will reach peak global impact.
Eclipse Now 