The costs of climate change are often estimated in monetary terms, but this raises ethical issues. Here we express them in terms of numbers of people left outside the 'human climate niche'-defined as the historically highly conserved distribution of relative human population density with respect to mean annual temperature. We show that climate change has already put similar to 9% of people (>600 million) outside this niche. By end-of-century (2080-2100), current policies leading to around 2.7 degrees C global warming could leave one-third (22-39%) of people outside the niche. Reducing global warming from 2.7 to 1.5 degrees C results in a similar to 5-fold decrease in the population exposed to unprecedented heat (mean annual temperature >= 29 degrees C). The lifetime emissions of similar to 3.5 global average citizens today (or similar to 1.2 average US citizens) expose one future person to unprecedented heat by end-of-century. That person comes from a place where emissions today are around half of the global average. These results highlight the need for more decisive policy action to limit the human costs and inequities of climate change.