Scholars have sought to quantify the extent of inequality which is inherited from past generations in multiple ways, including a large body of work on intergenerational mobility and inequality of opportunity. This paper makes two contributions to that broad literature. First, we show that many of the most frequently used approaches to measuring mobility or inequality of opportunity fit within a general framework which involves, as a first step, a calculation of the extent to which inherited circumstances can predict current incomes. Second, we suggest a new method - within that broad framework - which is sensitive to differences across the entire distributions of groups with different inherited characteristics, rather than just in their means. This feature makes it particularly well-suited to measuring inequality of opportunity, as well as to any inequality decomposition approach that requires going beyond means in assessing between-group differences. We apply this approach to South Africa, arguably the world's most unequal country, and find that almost three-quarters of its current inequality is inherited from predetermined circumstances, with race playing the largest role but parental background also making an important contribution.