Joint Life Expectancy Calculator

Years	Either Alive %	Both Alive %	First Person %
5	$99.55	$86.32	$90.81
10	$97.26	$68.36	$78.14
15	$90.96	$47.16	$61.79
20	$77.65	$26.05	$42.72
25	$55.86	$10.01	$23.81
30	$29.80	$2.10	$9.31
35	$9.66	$0.16	$1.99
40	$1.34	$0.00	$0.14
45	$0.03	$0.00	$0.00
50	$0.00	$0.00	$0.00

Quick Answer: For a male aged 65 and a female aged 63, there is a 29.8% chance at least one of them is alive in thirty years -- at ages 95 and 93. Individually the odds are only 9.3% and 22.6%. The couple's horizon is 7.2 percentage points longer than the stronger individual's, which is exactly the longevity risk single-life planning misses.

Overview

For a couple, the money has to last until the last survivor dies, not until either individual's life expectancy. Those are very different horizons, and planning to the wrong one is a systematic error.

The arithmetic is unintuitive. Two people each with a modest chance of reaching a given age have a substantially higher combined chance that at least one of them does. Here, a 9.3% and a 22.6% individual probability combine to 29.8%.

The gap widens as the horizon shortens. Over twenty-five years the joint probability is 55.9% -- better than even that one of them is still alive, and still spending.

This page reads mortality from the SSA period life table held in the engine rather than assuming a fixed horizon.

How This Is Calculated

Individual survival to a target age is the product of annual survival rates drawn from the SSA table:

p_i = \prod_{t=0}^{n-1} \left(1 - q_{age+t}\right)

The two lives are then combined assuming independence:

P(\text{both}) = p_1 \times p_2

P(\text{at least one}) = 1 - (1 - p_1)(1 - p_2)

So for the default couple: both alive is 0.093 × 0.226 = 2.1%, and at least one alive is 1 − (0.907 × 0.774) = 29.8%.

Worked Example

Male 65, female 63, thirty-year horizon:

He reaches 95: 9.3%
She reaches 93: 22.6%
Both alive: 2.1%
At least one alive: 29.8%
Remaining life expectancy: 18.1 years for him, 22.3 for her

Over twenty-five years instead: the joint probability rises to 55.9%. A couple planning only to their individual life expectancies would have run out well before the point at which one of them is more likely than not still living.

Both aged 55, forty-year horizon: 22.3% that one reaches 95. Early retirement lengthens the horizon substantially.

Two women rather than a mixed couple: 35.1% at the same ages, because female mortality is lower at every age in the table.

What This Does Not Account For

Independence. The calculation assumes the two lives are statistically independent. In reality couples share environment, habits and healthcare access, and there is a well-documented widowhood effect. True joint survival is slightly different from the product of two independent probabilities.
Individual health. Population tables say nothing about your own circumstances. Smoking status, chronic conditions and family history move these figures far more than the averages suggest.
Socioeconomic gradient. Life expectancy varies substantially by income and education, and the SSA table is a national average across all of them.
Future mortality improvement. Period tables use current rates. If mortality continues improving, these probabilities understate survival.
Annuity and pension pricing, which uses insurer tables with different assumptions and loadings.
Required Minimum Distribution joint tables, which are prescribed by the IRS and differ from these figures.
The financial consequences. This gives a horizon, not a plan. Pair it with the retirement Monte Carlo simulator to test whether the money lasts that long.

Common Pitfalls

Planning to one person's life expectancy. For a couple this is the single most common and most expensive error. Money is needed until the last survivor dies.
Planning to the average of the two. The relevant figure is the maximum, not the mean, and probabilistically it is longer than either.
Treating life expectancy as a deadline. It is a median. Roughly half of people outlive it, which is precisely the risk being planned against.
Ignoring the survivor's changed finances. The last survivor typically loses one Social Security benefit and may lose pension income, while household costs fall by much less than half.
Assuming the joint figure is just the higher individual one. It is meaningfully higher: 29.8% against 22.6% here.
Using population averages for an individual in poor or excellent health. These are national averages and should be adjusted by judgement.

Frequently Asked Questions

Why is the joint probability higher than either individual one?

Because it only takes one of them to survive. The chance that neither does is the product of the two failure probabilities, and 0.907 × 0.774 is 0.702, so 29.8% remains.

What planning horizon should a couple use?

Longer than either individual life expectancy. Many planners use the age at which joint survival falls to 10% or 25%. For this couple, twenty-five years still carries a 55.9% chance one is alive, so thirty years is a reasonable but not conservative horizon.

Does this assume the two deaths are independent?

Yes, and that is a simplification. Couples share environment and habits, and bereavement itself affects mortality. The independence assumption is standard but not exact.

Why do the sexes differ so much?

Female mortality is lower at essentially every age in the SSA table. Here a woman two years younger has a survival probability roughly two and a half times the man's over the same horizon.

Is this the same as the IRS joint life table?

No. The IRS prescribes its own joint and last survivor tables for Required Minimum Distributions, with different construction and purpose. These figures are for planning horizons, not RMD calculation.

Should I use this instead of my own health information?

No. These are population averages. Personal and family health history should move your working assumption substantially in either direction.

Sources

SSA period life table, held in engine/tables and verified against the primary source during the corpus data sweep.
Joint survival is computed as one minus the product of the two individual failure probabilities, the standard independence assumption.
Remaining life expectancy figures are read from the same table by age and sex.

Joint Life Expectancy Calculator (Last Survivor Planning Horizon)

Assumptions

Preset scenarios

Horizon vs Survival Probability

Survival Probability by Horizon