Abstract The concept of radiation-induced aging is revisited from the viewpoint of a mathematical model. The effect of radiation on carcinogenesis is treated based on the Armitage–Doll multi-stage theory. The formula obtained for cancer incidence rate indicates that radiation dose can be explained in terms of time. Radiation-induced aging for acute and chronic exposures is described using age-specific cancer incidence rates as a measure of aging. It shows that accelerated aging is related to the dose rate, whereas premature aging is related to the cumulative dose, providing a simple and natural interpretation of radiation-induced aging. The usefulness of this approach is demonstrated by applying the formula to cancer prevalence data from mice chronically exposed to low dose-rate radiation.