Estimates of the Earth's carrying capacity for humans vary drastically, with most estimates ranging between 4 and 16 billion, according to Wikipedia. The Institute for Lifecycle Energy Analysis cites studies showing median estimates of carrying capacity that range from 7.7 to 12 billion people.
Wikipedia explains that carrying capacity refers to the maximum population that the Earth can sustain indefinitely. Factors affecting carrying capacity include population increases and decreases, availability of food and water, sanitation and health care. According to the Jrank Science Encyclopedia, the ideal or optimal carrying capacity occurs when birth and death rates are equal and the population size is in equilibrium with its environment, which does not actually occur in nature.