Wet-bulb globe temperature (WBGT)–a standard measure for workplace heat stress regulation–incorporates the complex, nonlinear interaction among temperature, humidity, wind and radiation. This complexity requires WBGT to be calculated iteratively following the recommended approach developed by Liljegren and colleagues. The need for iteration has limited the wide application of Liljegren’s approach, and stimulated various simplified WBGT approximations that do not require iteration but are potentially seriously biased. By carefully examining the self-nonlinearities in Liljegren’s model, we develop a zero-iteration analytic approximation of WBGT while maintaining sufficient accuracy and the physical basis of the original model. The new approximation slightly deviates from Liljegren’s full model—by less than 1oC in 99\% cases over 93\% of global land area. The annual mean and 75-99\% percentiles of WBGT are also well represented with biases within ±0.5oC globally. This approximation is clearly more accurate than other commonly used WBGT approximations. Physical intuition can be developed on the processes controlling WBGT variations from an energy balance perspective. This may provide a basis for applying WBGT to understanding the physical control of heat stress.