Nucleate boiling has significant applications in earth gravity( in industrial cooling applications) and micro-gravity conditions (in space exploration, specifically in making space applications more compact). However, the effect of gravity on the growth rate and bubble size is not yet well understood. We perform numerical simulations of nucleate boiling using an adaptive Moment-of-Fluid (MoF) method for a single vapor bubble (water or Perfluoro-n-hexane) in saturated liquid for different gravity levels. Results concerning the growth rate of the bubble, specifically the departure diameter and departure time have been provided. The MoF method has been first validated by comparing results with a theoretical solution of vapor bubble growth in super-heated liquid without any heat-transfer from the wall. Next, bubble growth rate, bubble shape and heat transfer results under earth gravity, reduced gravity and micro-gravity conditions are reported and they are in good agreement with experiments. Finally, a new method is proposed for estimating the bubble diameter at different gravity levels. This method is based on an analysis of empirical data at different gravity values and using power-series curve fitting to obtain a generalized bubble growth curve irrespective of the gravity value. This method is shown to provide a good estimate of the bubble diameter for a specific gravity value and time.