What does justice require of regulators? Various executive orders enjoin health and safety regulators to take account of distributive impacts, equity, or justice, and many scholars endorse these requirements. But concrete methodologies for evaluating the equity effects of regulation policies remain undeveloped. The contrast with cost-benefit - now a very well developed set of techniques - is stark. Equity by governmental agencies that regulate health and safety risks, at least in the United States, lacks rigor and structure.This Article proposes a rigorous framework for risk-equity analysis, which I term probabilistic population profile analysis (PPPA). PPPA is both novel, yet firmly grounded in the social-welfare-function tradition in welfare economics. The PPPA framework conceptualizes both the status quo, and possible policies, as probability distributions across population profiles - where each population profile is, in turn, a concatenation of lifetime health-longevity-income histories, one for each member of the population. A utility function transforms each such profile into a utility vector. An equity-regarding social welfare function (SWF) is then specified. Policy analysts can employ the equity-regarding SWF both (1) to determine how policies compare purely as a matter of equality; and (2) to determine how they compare all-things-considered, considering both equality and overall welfare. The proposal may seem utopian, but is not. Scholars in the field of optimal tax policy already use SWFs to evaluate policies. Characterizing policies as distributions across population health-longevity-income profiles builds on existing assessment and general-equilibrium-modeling techniques. Utility functions can be specified through survey research and, in the interim, by building on standard functional forms. Plausible normative axioms considerably narrow the possible forms of the SWF, and survey research or thought experiments narrow the field further. Part I of the Article describes and criticizes existing approaches to equity that have been proposed in the scholarly literature: the environmental justice conception of equity; individual risk approaches; QALY-based equity analysis; incidence analysis; inclusive equality measurement; and cost-benefit with weights. Part II describes and defends PPPA. PPPA has many virtues. It recognizes that well-being is multidimensional, a function of both income and health/longevity; furnishes a metric for inequality; provides a framework for making tradeoffs between equality and overall well-being; and understands that justice includes (but is not limited to) inequalities between high and low-status social groups.