A method for calculating the fugacity of pure sulfur in the alpha-solid, beta-solid and liquid phase regions has been reported for application to industrial equilibrium conditions, e.g., high-pressure solubility of sulfur in sour gas. The fugacity calculations are self-consistent with the low-pressure phase diagram. As recently discussed by Ferreira and Lobo [1], empirical fitting of the experimental data does not yield consistent behaviour for the low-pressure phase diagram of elemental sulfur. In particular, there is a discrepancy between the vapour pressure of beta-solid (monoclinic) and liquid sulfur at the fusion temperature. We have provided an alternative semi-empirical approach which allows one to calculate values of the fugacity at conditions removed from the conditions of the pure sulfur phase transitions. For our approach, we have forced the liquid vapour pressure to equal the beta-solid vapour pressure at the beta-l-g triple point corresponding to the 'natural' fusion temperature for a-solid. Many studies show a higher 'observed' fusion temperature for elemental sulfur. The non-reversible conditions for 'observed' fusion conditions for elemental sulfur result from a kinetically hindered melt which causes some thermodynamic measurements to be related to a metastable S(8) liquid. We have measured the 'natural' fusion temperature, T(fus)(beta)(exp.) = (388.5 +/- 0.2) K at p = 89.9 kPa, which is consistent with literature fusion data at higher-pressures. Using our semi-empirical approach, we have used or found the following conditions for the low-pressure sulfur phase diagram: T(alpha-beta-g) = 368.39 K, p(alpha-beta-g) = 0.4868 Pa, T(alpha-beta-g) = 388.326 K, p(alpha-beta-g) = 2.4437 Pa, T(fus)(beta-1)(101325 kPa) = 388.348 K, T(alpha-beta-I) = 419.06 K, and p(alpha-beta-I) = 124,360 kPa. (C) 2011 Elsevier Ltd. All rights reserved.