The primary risk coefficients upon which exposure limits for radiation protection purposes are currently based are derived almost exclusively from cancer-induction data obtained from human populations exposed to radiations of low linear energy transfer. The question of higher linear energy transfer radiations is handled by means of quality factors derived from values for relative biological effectiveness obtained from animal data. However, the advent of microdosimetry has made it possible to establish hit size effectiveness functions from single-cell systems, both in vitro and in vivo. This type of function can substitute completely for the concept of relative biological effectiveness, Q and equivalent dose. A common basis for risk coefficients and the hit size effectiveness function lies in the fact that human cancers are monoclonal and thus single cell in origin. The present communication utilizes this common base as a means of extending the present low-linear energy transfer based risk coefficients to include carcinogenic responses from exposure in radiation fields of any one or mixed qualities, extending from the smallest to the largest linear energy transfers of practical consequence. In doing so, risks from ionizing radiations of any linear energy transfer may be predicted more accurately than at present.