Life expectancy is the most quoted number in retirement planning, and the most misread. This page, part of our guides to how the maths works, explains exactly what it measures, the two ways actuaries define it, and why it is a poor stand-in for how long any one person should plan for.
The idea in plain English
Take everyone who is exactly 65 today. Some will die next year, some will reach 100. Life expectancy at 65 is the average of all those remaining lifetimes, worked out from a life table as if its death rates held for the rest of their lives.
Three things follow from that definition:
- It is an average, not a forecast. It describes a group. Nobody is “expected” to die on the date it points to.
- It changes as you age. Reaching 65 means you have already avoided every death before 65, so your expected age at death is higher than it was at birth. For men in the SSA 2023 table, life expectancy at birth is 75.8 years, but a man who reaches 65 can expect 18.12 more, to about 83.1.
- Many people outlive it. Ages at death bunch up in the 80s and 90s with a long tail of earlier deaths, which pulls the average below the middle. At 65, 53% of men and 54% of women in the table live past their life expectancy.
The notation
Write Future lifetime TₓThe number of years, including part years, that someone aged x will go on to live. Unknown in advance, so it is treated as a random quantity.How it works: Life expectancy for the future lifetime of someone aged Age xYour age today, in whole years.How it works: Life tables, in years and part years, and Curtate future lifetime KₓThe number of whole years someone aged x will go on to live: Tₓ rounded down.How it works: Life expectancy for the whole years only. Neither is known in advance; the life table gives their probabilities.
- Complete life expectancy e̊ₓThe average number of years still to live for someone aged x, counting part years. The ring marks the complete version.How it works: Life expectancy (e-ring): the complete expectation of life, the average of . The ring marks “complete”. This is what the SSA and most published tables print.
- Curtate life expectancy eₓThe average number of whole years still to live for someone aged x. It is about half a year less than the complete figure.How it works: Life expectancy: the curtate expectation of life, the average of , counting whole years only.
- Survival probability ₜpₓThe chance that someone aged x is still alive t years from now.How it works: Survival probability: the chance of surviving years, from survival probability.
The formulas
The average of a lifetime equals the sum of the chances of being alive at each moment along the way:
Complete: area under the survival curve. Curtate: survival added up at each future birthday.
With deaths spread evenly within each year of age (UDD), survival is a straight line between birthdays, so each year contributes the average of its start and end values. That gives the formula the calculators use:
Under UDD the difference is exactly half a year, because the year-of-death probabilities add up to 1.
The half comes from those who die in each year living, on average, half of it. The curtate figure is useful for valuing payments made once a year; the complete one is the natural “average years left”.
Worked example: men and women aged 65
From the SSA 2023 period table, using the engine that runs the calculators:
- Complete life expectancy for a man aged 65: = 18.12 years. The SSA prints 18.12, so the UDD calculation reproduces the official figure.
- Curtate: = 17.62 years, 0.50 years less.
- The median remaining lifetime, the point where survival falls to one half, is 18.8 years (to about age 84). It is longer than the average because the early deaths pull the average down.
- 53% of men aged 65 live past the expectancy.
- For a woman aged 65: 20.66 years against a printed 20.66, and 54% live past it.
Try it: complete, curtate and the spread
Pick an age and sex. The bars show the chance of dying in each future year of age, Deferred death probabilityThe chance that someone aged x survives k years and then dies in the year after: kpₓ times qₓ₊ₖ.How it works: Survival probability; the solid line is the life expectancy and the dashed line the median. The darker bars are deaths after the expectancy.
Life expectancy: complete, curtate and the spread
- Complete,
- 18.1 yrsto about age 83
- Curtate,
- 17.6 yrswhole years only
- Difference
- 0.50 yrsexactly ½ under UDD
- SSA printed figure
- 18.12 yrscomplete expectancy
- Median remaining life
- 18.8 yrshalf live past 84
- Chance of outliving it
- 53%live past the expectancy
- Deaths in each year of age,
- Deaths after the expectancy
- Expectancy, age 83.1
- Median, age 83.8
Source: US Social Security Administration, 2023 period life table (Period Life Table, 2023, as used in the 2026 Trustees Report). Do My Numbers calculations.
Period and cohort life expectancy
Every figure on this page is a period life expectancy: it applies the death rates of 2023 at every future age. A cohort life expectancy follows people born in one year and uses the death rates projected for them as they age, including future improvements. Because death rates have mostly fallen over time, cohort figures are usually higher than period ones. The SSA publishes both; the Trustees Report sets out the projections behind the cohort tables.
Neither is a forecast for an individual. Health, smoking, income and family history all move a person’s chances away from the population average, and future medicine is unknowable.
Where life expectancy is, and isn’t, the right number
Life expectancy is the right summary for comparing groups or years. For planning how long money must last, the whole survival curve matters more: the how long will my money last calculator reports the chance of being alive when savings run out, rather than comparing against a single age. The life expectancy by age table shows the figures for every age, and the life expectancy calculator works them out for one person or a couple.
The IRS life expectancy tables used for required minimum distributions are a different set: they come from a mortality basis the IRS sets in regulations, not from the SSA table, and they are used to divide a balance, not to describe anyone’s lifespan. See the IRS life expectancy tables.
Where this is used
Questions
What is life expectancy?
Life expectancy at a given age is the average number of further years that people of that age would live if the death rates in a life table applied to them for the rest of their lives. It is an average over everyone of that age, not a prediction for any one person.
Why do many people live longer than their life expectancy?
Because life expectancy is an average, and the spread of ages at death is wide and lopsided. Some people die young, which pulls the average down, so at retirement ages more than half of people outlive the average. That is why planning to an age around life expectancy leaves a large chance of living longer.
What is the difference between complete and curtate life expectancy?
Complete life expectancy, written e̊ₓ, counts every part of a year lived. Curtate life expectancy, eₓ, counts only whole years. If deaths are spread evenly within each year of age, the complete figure is exactly half a year more than the curtate one.
What is the difference between period and cohort life expectancy?
Period life expectancy uses the death rates of a single year at every age, as if they never changed. Cohort life expectancy uses the death rates expected for people born in a given year as they age, including expected improvements, so it is usually higher.