Despite the importance of public opinion for policy formation and the political salience of inequality, the public’s views about the desirability of equality, not only in health but also in economics and politics, has attracted little attention. We report the results of an on-line survey administered in late 2016 in Great Britain (N=1667 with a response rate of 35- 50%). The survey allowed for testing the sensitivity of public opinion across two other variables: absolute versus relative (everyone should have the same versus inequality should be reduced) and bivariate versus univariate (inequality in one domain is judged in relation to inequality in another versus inequality in a domain is judged independently of other domains). It also allowed examination of how far support for equality in one domain overlaps with support for equality in another. We find that for health, economic and political equality a relative conception of equality attracts more support than an absolute conception, and that for health and political equality a bivariate conception attracts more support than a univariate conception. We also find that conceptions of equality affect how much overlap exists between support for different forms of equality, with a bivariate and relative conception resulting in more overlap than a univariate and absolute conception. We also find evidence for Walzer’s ‘complex equality’ theory in which people tolerate inequality in one domain if it does not control inequality in another.