Force of Mortality Calculator

How it is calculated

The tool evaluates the Gompertz hazard μ(x) = B × cx, where B is the baseline hazard at age 0 (per year), c is the growth factor per year of age and x is the age in years. It then converts the rate into an approximate one-year death probability with qx ≈ 1 − e−μ(x). Because the hazard grows by the factor c each year, it doubles every ln 2 ÷ ln c years, about 7.3 years when c = 1.1.

B and c must be greater than zero and the age cannot be negative. The age may include decimals and is used exactly in the calculation, although the summary line rounds it to a whole number. The tool does not fit B and c to data; you must supply parameters from a table or model of your own. Also note that μ is a rate, not a probability, and the q figure assumes the hazard stays constant over the year.

Common mistakes

• Reading μ(x) as a probability. It is a rate per year; the probability of dying in the year is the separate q figure, which is always smaller for large rates.
• Entering B as a percentage (0.003 for 0.003%). B is a plain fraction per year, so a baseline of 3 in 100,000 is 0.00003.
• Using c = 10 or c = 0.1 because it looks like a percentage. For human adults c is just above 1, since the hazard grows by a few percent of itself each year; the tool also accepts values below 1, but those model falling mortality, which is not Gompertz ageing.
• Applying parameters fitted to one population, sex or period to another. B and c change with each, so results are only as good as the parameters.
• Using the model at young ages. Gompertz describes ageing mortality and ignores infant and accident mortality, so results at age 0 to 20 are not realistic.