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Human mortality has a shape. After early adulthood the annual risk of dying rises roughly exponentially, doubling every eight years or so, and on top of that sits a flat term for the deaths that have nothing to do with ageing. Those two components are separate levers, and they pay out very differently.
h(t) = A·eG·t + M
A sets where the ageing hazard starts, G how fast it compounds, M how much death is unrelated to age. Survival is S(t) = exp(−∫h), integrated numerically. The doubling time you set is G expressed the way people actually quote it: G = ln2 / doubling time.
The baseline. Doubling time near eight years, extrinsic mortality down to a few hundredths of a percent per year.
How long it takes the annual risk of dying to double. Human populations sit near eight years and have barely moved in a century. This is the ageing rate itself.
Deaths per 100,000 per year that do not rise with age: accidents, infection, violence. Around 50 in a rich country today, well over 1,000 in 1900.
Where the ageing hazard starts, as a multiple of the calibrated baseline. Lowering it shifts the whole curve right without changing its slope — the effect a one-off repair would have.
G = ln2 / 8.0 = 0.0866 yr⁻¹
A = 4.117e-5 yr⁻¹
M = 5.000e-4 yr⁻¹
age 8059.1% baseline59.1% scenario
| Metric | Baseline | This scenario | Change |
|---|---|---|---|
| Life expectancy at birth | 80.0 | 80.0 | ±0.0 yr |
| Remaining life at 40 | 42.0 | 42.0 | ±0.0 yr |
| Remaining life at 60 | 24.5 | 24.5 | ±0.0 yr |
| Remaining life at 80 | 10.8 | 10.8 | ±0.0 yr |
| Median survival age | 83.4 | 83.4 | ±0.0 yr |
| Chance of reaching 100 | 6.1% | 6.1% | ±0.0 pts |
Baseline is fixed at 8.0 yr doubling time, 50 /100k/yr extrinsic, 1.00× A. Expectancies are truncated at age 200.
Gompertz–Makeham is the standard first model of adult mortality and it is wrong in known, specific ways. Here they are. Any number this page produces inherits all of them.
The Gompertz term is tiny at age 0 and rises from there, so the model puts almost no deaths in childhood. Real hazard is high at birth, bottoms out around age 10, and only then starts compounding. Below about age 30 this curve is optimistic.
Observed mortality stops accelerating somewhere past 105 and may plateau. This model keeps doubling forever, so it undercounts supercentenarians at long doubling times.
Everyone here has identical parameters. Real populations are mixtures of frailties, and the frail die first, which bends the aggregate hazard downward at old ages even when no individual's hazard bends.
The three sliders apply unchanged from birth to death. No real cohort experiences that — mortality conditions change underneath you as you age.
That is what makes it the Makeham term. Actual accident and infection mortality is not flat: it spikes in young adulthood and again in late old age.
A was chosen by bisection so the baseline lands on 80.0 years at birth. It is not measured from a life table, and nothing downstream of it should be quoted as a fact about any population.
Trapezoidal integration of the hazard on a monthly grid to age 200. Life expectancies are truncated there, which matters only for scenarios that push median survival past about 150.
The longest duration a human being has lived or could live, distinct from average life expectancy and disputed as to whether any fixed ceiling exists.
The consensus taxonomy of cellular and molecular processes held to drive mammalian aging, set out as nine mechanisms in 2013 and expanded to twelve in 2023.
The hypothesis that chronic illness can be postponed into a shorter interval before death, so that added years of life are healthy ones.
The portion of life spent in good health and function, as distinct from total lifespan; widely used as a goal but not standardized as a measure.
The companion model is the escape-velocity simulator, which asks what happens if the parameters on this page keep improving while you are alive rather than staying fixed.