Future economic growth will affect societal well-being and the environment, but is uncertain. We describe a multidecadal pattern of GDP per capita growth rising, then declining, as regions become richer. A fitted differential-equation model (DEM) and an integrated assessment model (International Futures, IFs) accounting for this pattern both predict 21st-century economic outlooks with slow growth and income convergence compared to the widely used Shared Socioeconomic Pathways (SSPs)—similar to SSP4 (‘Inequality’). For World Bank income groups, the DEM could have produced, from 1980, consistent projections of 2100 GDP per capita, and more accurate predictions of 2010s growth rates than the International Monetary Fund (IMF)’s short-term forecasts. DEM and IMF forecasts were positively biased for the low-income group. SSP4 might therefore represent a best-case—not worst-case—scenario for 21st-century growth and income convergence. IFs projects high poverty and population growth, and moderate energy demands and CO2 emissions, within the SSP range.