AbstractChanging the mortality risks we face would change human life expectancy. As a special case, one could imagine adding a fixed incrementRto all the age-specific mortality rates from age zero upwards. For this case we seek a constantK(A) such thatK(A) xRapproximates the resulting change in life expectancy remaining at ageA, at least for small values ofR. The formula forK(A) derived here corrects a heuristic argument that appeared in JORS earlier. An estimate ofK(0) suggests that the permanent addition of a one-in-a-million risk at each year of life would reduce life expectancy at birth by about 1 day—a useful fact for risk communication.