An axisymmetric numerical model has been developed to conduct a study of single droplet evaporation over a wide range of ambient pressures both under normal and microgravity conditions. Results for droplet lifetime as a function of ambient pressure and initial droplet diameter are presented. The enhancement in the droplet evaporation rate due to natural convection is predicted. This enhancement becomes more dominant with increasing ambient pressure due to the increase in the Grashof number. The higher the ambient pressure, the closer the Grashof number remains to its initial value throughout most of the droplet lifetime because of the droplet swelling and the heat-up of the droplet interior. Results should be particularly of interest to researchers conducting experiments on droplet evaporation at elevated pressures within a normal gravity environment. The model developed is in good agreement with experimental data at low pressures. Explanations have been provided for its deviation at high pressures.