Grain size in the Earth's upper mantle is a fundamental parameter that has crucial implications on large-scale processes, such as the permeability and the rheology of rocks. However, grain size is constantly evolving with time, where static grain growth implies an increase of the average grain size whereas dynamic recrystallization contributes to its decrease. Static grain growth is most dominant in grain size-sensitive deformation regimes and is classically defined by a grain growth law of the form:rfn - rin = k twith rf and ri, the final and initial grain radii, n the grain size exponent, t the duration, k the grain growth rate. These growth parameters are highly dependent on the value of n, which has considerable implications when extrapolating from laboratory to geological length and time scales. Here, we will show that there is no clear n value that can be extracted from grain growth experiments and that this value must be fixed based on the appropriate theoretical background. We have therefore investigated static grain growth of olivine aggregates where the intergranular medium is dry, wet or contains melt. Grain growth experiments were performed and modeled by considering different growth mechanisms (i.e. diffusion-limited and interface reaction-limited). We have established the dry grain growth law from previously published experiments at 1-atm and high-temperature conditions. Grain growth rates for these samples are limited by Si diffusion at grain boundaries (GB), implying n = 2. On the contrary, experiments on melt- and H2O-bearing aggregates indicate faster growth rates than for dry samples, regardless of the liquid fraction (i.e. >0%). We propose a general grain growth law, which takes into account dry GB as well as wetted grain-grain interfaces, by using the wetting properties of the liquid phase as shown by our high-resolution images. We show that our unified grain growth law considerably deviates from the classical grain growth law, with critical differences at geological time scales. We expect that our law will help unravel physical properties that are dependent on processes happening at the GB scale, such as rheology, diffusion or permeability.