PurposeThis study tests convergence in energy diversification, per-capita income and financial development and explores their interrelationships.Design/methodology/approachClub convergence tests, Granger tests and panel regressions are employed on 134 countries from 1995 to 2019.FindingsWhile overall convergence is absent across the entire sample, countries have converged within specific clubs. Low- and lower-middle-income countries show convergence in energy diversification and per-capita income. Positive bidirectional relationships are found between energy diversification and per-capita income, and between financial development and per-capita income. A U-shaped relationship between oil prices and energy diversification is identified.Research limitations/implicationsThe findings suggest that achieving a shared equilibrium in energy diversification, economic prosperity and financial development is feasible through technological progress within convergence clubs. Investments in human capital and technology are crucial prerequisites for sustainable development.Originality/valueThis study pioneers testing energy diversification, per-capita income and financial development convergence, investigating the tri-directional relationship between them, and exploring the U-shaped relationship between oil prices and energy diversification.