In this paper, we present a Capabilities-based Approach to the acceptability and the tolerability of risks posed by natural and man-made hazards. We argue that judgments about the acceptability and/or tolerability of such risks should be based on an evaluation of the likely societal impact of potential hazards, defined in terms of the expected changes in the capabilities of individuals. Capabilities refer to the functionings, or valuable doings and beings, individuals are able to achieve given available personal, material, and social resources. The likely impact of a hazard on individuals' capabilities should, we argue, be compared against two separate thresholds. The first threshold specifies the minimum level of capabilities attainment that is acceptable in principle for individuals to have in the aftermath of a hazard over any period of time. This threshold captures the level that individuals' capabilities ideally should not fall below. A risk is acceptable if the probability that the attained capabilities will be less than the acceptable level is sufficiently small. In practice, it can be tolerable for some individuals to temporarily fall below the acceptable threshold, provided this situation of lower capabilities attainment is temporary, reversible, and the probability that capabilities will fall below a tolerability threshold is sufficiently small. This second, tolerable threshold delimits an absolute minimum level of capabilities attainment below which no individual in a society should ever fall, regardless of whether that level of capabilities attainment is temporary or reversible. In this paper, we describe and justify this Capabilities-based Approach to the acceptability and tolerability of risks. We argue that the proposed theoretical framework avoids the limitations in current approaches to acceptable risk. The proposed approach focuses the attention of risk analysts directly on what should be our primary concern when judging the acceptability and the tolerability of risks, namely, how risks impact the well-being of individuals in a society. Also, our Capabilities-based Approach offers a transparent, easily communicable way for determining the acceptability and the tolerability of risks.