Force of Mortality Calculator

About this calculator

The force of mortality, written μ(x), is the instantaneous rate at which a person aged exactly x is dying at that moment — the continuous-time analogue of the annual mortality rate q_x used in life tables. The Gompertz law, proposed in 1825, models this hazard as growing exponentially with age: μ(x) = B · c^x, where B sets the baseline hazard and c (typically around 1.08–1.11 for human adult mortality) controls how fast risk doubles with each additional decade.

Gompertz's model remains a good fit for adult mortality from roughly age 30 onward and underlies much of actuarial mortality modeling, including extensions like the Gompertz–Makeham law that adds a constant term for age-independent causes of death. Because μ(x) is a rate rather than a probability, this calculator also converts it to an approximate annual death probability via q_x ≈ 1 − e^(−μ(x)), the standard bridge actuaries use between the continuous hazard and the discrete life-table figure.