We develop a normative approach to the measurement of inequality of opportunity. This means that we measure inequality of opportunity by the welfare gain in moving from the actual income distribution to the optimum income distribution with the given amount of total income. Our study combines several approaches present in the literature: we axiomatically characterize social welfare functions, we obtain several allocation rules as optima and we obtain several inequality measures. Our analysis reflects moreover the main distinctions in the literature: ex post versus ex ante compensation and liberal versus utilitarian reward.