Expectation Of Life Calculator

Work out expectation of life instantly with clear inputs, formula shown and shareable results.

About Expectation Of Life Calculator

Expectation of life is the average number of further years lived. Under a constant annual mortality rate the curtate expectation collapses to pₓ/qₓ, and adding half a year gives the complete expectation that allows for deaths part-way through a year.

Formula

Constant-force expectation

eₓ = p/q; e°ₓ = eₓ + 0.5; ₁₀pₓ = p^10

p: Survival rate
q: Mortality rate

Worked example

With the default values below, Expectation Of Life Calculator returns Complete Expectation Of Life of 39.50. Change any input above and every figure here is recalculated in your browser.

Inputs used

Current Ageaccepts 0–110: 65
Assumed Annual Mortality Rateaccepts 0.01–60 %: 2.5 %

Results

Complete Expectation Of Life: 39.50 years
Curtate Expectation (eₓ): 39.00 years
Implied Age At Death: 104.5 years
Chance Of Surviving 10 More Years: 77.63%

Step by step

1Values used
2Constant-force expectation
3Complete Expectation Of Life= 39.50 years
4Curtate Expectation (eₓ)= 39.00 years
5Implied Age At Death= 104.5 years
6Chance Of Surviving 10 More Years= 77.63

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why add half a year?

Curtate expectation counts only whole years survived. Deaths occur on average mid-year, so the complete figure adds about 0.5.

Is constant mortality realistic?

Only over short spans. Real mortality rises steeply with age, so a full life table gives a better answer at older ages.