Estimates of global economic damage from climate change assess the effect of annual temperature changes. However, the roles of precipitation, temperature variability and extreme events are not yet known. Here, by combining projections of climate models with empirical dose–response functions translating shifts in temperature means and variability, rainfall patterns and extreme precipitation into economic damage, we show that at +3 °C global average losses reach 10% of gross domestic product, with worst effects (up to 17%) in poorer, low-latitude countries. Relative to annual temperature damage, the additional impacts of projecting variability and extremes are smaller and dominated by interannual variability, especially at lower latitudes. However, accounting for variability and extremes when estimating the temperature dose–response function raises global economic losses by nearly two percentage points and exacerbates economic tail risks. These results call for region-specific risk assessments and the integration of other climate variables for a better understanding of climate change impacts.