If humanity does not go prematurely extinct, then the number of people who will ultimately exist could be astronomical. These figures are useful for judging the value of work that influences the long-term future, and in particular for judging how important it is to avoid existential risks.
Nick Bostrom argues that, barring disaster, Earth will capable of sustaining life for approximately another billion years (Bostrom 2012). This means that if Earth’s population were to remain fairly close to what is today, then, assuming hundred-year life-spans, the planet would ultimately host about 1016 (“a million billion”) people.
This is not an upper-bound on the possible number of people, however. If humans are ultimately able to colonize other star systems, then they will not be limited by Earth’s ability to sustain life. One model created by Bostrom, based on plausible estimates of cosmological parameters, implies that there could ultimately be 1032 (“a hundred thousand billion billion billion”) humans of normal life-span.
Though these numbers are surrounded by high levels of uncertainty, they do strongly suggest that the number of future people could be overwhelmingly greater than the number of people who have lived so far—and, a fortiori, than the number of people currently alive.
Botrom, Nick. 2012. Existential risk prevention as a global priority. Global policy 4(1): 15-31.
An attempt to justify these estimates in greater depth, and to highlight the importance of existential risk prevention.