Online datasets have the potential to change the prevailing reality in the global measurement of many socio-economic statistics. Facebook has an expanding global presence, with more than 1 billion people using the platform daily. Differences in the way men and women use Facebook can provide measures for deep-seated structures of gender inequality. Particularly in countries with high-levels of gender disparity, women and men are using Facebook's platform in different ways and amounts. Building upon this observation, we use Facebook data and machine learning methods to predict measurements of global gender disparities, such as the Gender Inequality Index (GII) and the Social Institutions and Gender Index (SIGI). Our country-level predictions show a high degree of accuracy under cross-validation. We generalize our method to creating subnational estimates of the indices, which can be used by policy makers and development researchers to understand and improve levels of gender equality worldwide.