Per capita carbon emissions are an important concept in international negotiations of climate policies and also in future projections of aggregate carbon emissions. This paper argues that the convergence studies on per capita carbon emissions in the literature are theoretically biased because demographic structure is not considered. The paper therefore links demographic change to carbon convergence analysis and examines historical convergence of per capita carbon emissions for a global sample of countries over the period of 1960-2014. The results show that although demographic structure does not change the existence of carbon convergence, the growth of worker shares is significant in most estimations in this paper, and it also affects the estimates of the convergence speed. The time period of empirical analysis also matters for the convergence results. The paper further extends the IPAT identity by introducing demographic structure as well as economic and energy structure, and argues that the convergence of per capita carbon emissions depends on the convergence of each component, and each component may converge within different time horizons. The paper proposes that emissions rights should be allocated across countries based on a mix of long-term, medium-term and short-term rules.