Background Globally the trajectories of approaches in adoption and implementation of family planning programmes have varied subjecting to variation in cultural and political philosophies across the countries. Accordingly, the progress in family planning has varied over the time across the countries. Objective This study investigates long-term trajectories of demand for family planning and contraceptive prevalence rates and tests the hypothesis of convergence across the world countries. Methods This study used data from United Nations Population Prospects for 185 countries and regions during 1970-2015. Standard graphical, parametric and nonparametric convergence metrics have been used for testing of the convergence hypothesis. Results The results suggest a substantial increase in the global average of both demand and actual prevalence of contraceptive practice across the countries, but the actual contraceptive use is yet to catch up with the demand. Our findings suggest that there is a convergence in contraceptive use across the countries, particularly since the mid-1990s. Conclusion A major part of the convergence in demand for family planning and contraceptive prevalence rate is due to its stalling in both developed and many developing countries and its increase in several developing and least developed countries. Family planning has a greater role in human wellbeing particularly enhancing reproductive, maternal and child health outcomes than being a mere tool for fertility reduction. Therefore, the emphasis is needed on family planning efforts in the lagged behind countries for global convergence of family planning.