Recent studies have linked variability and extremes in temperature and precipitation to lower economic growth, but global GDP projections under climate change remain focused on annual temperatures. Here we combine empirical dose-response functions for temperature variability, rainfall deviations, and extreme precipitation with 33 CMIP6 models to examine GDP impacts under different warming levels. We find that at +3°C, global average losses amount to 8% of GDP, with the worst effects (up to 13%) in poorer, low-latitude countries. Relative to annual temperature damages, the additional GDP impacts of projecting variability and extremes are smaller and dominated by inter-annual variability, especially in lower latitudes. However, accounting for variability and extremes when estimating temperature dose-response functions raises global GDP losses by over 1%-pt. Since tail risks for economic growth are substantial, our results emphasize the need for region-specific risk assessments and reducing uncertainties around future variability and extremes, particularly for developing countries.