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Human life expectancy tends to be given as a single number reflecting age at death from birth.

But life expectancy should really grow the longer you live, because, for example, once you hit your fifth birthday your chances of dying before age five drop to zero, so the contribution to the average life expectancy of all the people who died before age five shouldn't apply.

To put it another way, once you hit age ninety, your life expectancy calculated then and there should be at least ninety years even though that exceeds the life expectancy in every country on the planet, simply because you've clearly already made it that far.

Does life expectancy as a function of current age have a name, and what shape does this function typically take? Perhaps more interestingly, does this function take a significantly different shape in humans than in other animals (I'd expect infant mortality to significantly affect this for example)?

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I think you might be looking for period life tables

A period life table is based on the mortality experience of a population during a relatively short period of time. Here we present the 2014 period life table for the Social Security area population. For this table, the period life expectancy at a given age is the average remaining number of years expected prior to death for a person at that exact age, born on January 1, using the mortality rates for 2014 over the course of his or her remaining life.

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