Occupational heat stress directly hampers physical work capacity (PWC), with large economic consequences for industries and regions vulnerable to global warming. Accurately quantifying PWC is essential for forecasting impacts of different climate change scenarios, but the current state of knowledge is limited, leading to potential underestimations in mild heat, and overestimations in extreme heat. We therefore developed advanced empirical equations for PWC based on 338 work sessions in climatic chambers (low air movement, no solar radiation) spanning mild to extreme heat stress. Equations for PWC are available based on air temperature and humidity, for a suite of heat stress assessment metrics, and mean skin temperature. Our models are highly sensitive to mild heat and to our knowledge are the first to include empirical data across the full range of warm and hot environments possible with future climate change across the world. Using wet bulb globe temperature (WBGT) as an example, we noted 10% reductions in PWC at mild heat stress (WBGT = 18°C) and reductions of 78% in the most extreme conditions (WBGT = 40°C). Of the different heat stress indices available, the heat index was the best predictor of group level PWC (R² = 0.96) but can only be applied in shaded conditions. The skin temperature, but not internal/core temperature, was a strong predictor of PWC (R² = 0.88), thermal sensation (R² = 0.84), and thermal comfort (R² = 0.73). The models presented apply to occupational workloads and can be used in climate projection models to predict economic and social consequences of climate change.