Coagulation of particles occurs when two particles collide and stick together. In the Martian atmosphere, coagulation of dust would increase the dust effective particle size, as small particles accrete to larger particles. Murphy et al. (1990) concluded that Brownian coagulation of dust in the Martian atmosphere was not significant, due to the low dust particle mixing ratios, while Montmessin et al. (2002) and Fedorova et al. (2014) showed that it mostly involves dust particle radii smaller than 0.1 μm. However, the effects of coagulation have never been explored in 3D, during a global dust storm, and in presence of larger numbers of small particles. Here we revisit this issue by using the NASA Ames Mars Global Climate Model (MGCM) to investigate the temporal and spatial changes in dust particle sizes during the 2018 global dust storm due to dust coagulation and the overall impact of these processes on Mars' climate. Our parameterization for dust coagulation includes the effect of Brownian motion, Brownian diffusion enhancement, and gravitational collection. We show that Brownian motion and Brownian diffusion enhancement dominate gravitational collection. Coagulation has a significant impact during the global storm, with coagulation rates increased by a factor of 10 compared to non-storm conditions. The mean effective particle radius can be increased by a factor of up to 2 due to coagulation, leading to a 20 K colder atmosphere above 30 km altitude. Overall, our parameterization improves the representation of the decay phase of the storm relative to MCS dust observations. Coagulation also remains a significant process affecting dust outside the storm period if large numbers of submicron-sized particles are involved. As coagulation removes the small sub-micron particles within a relatively short time, it may therefore be possible, in GCMs, to lift larger amounts of submicron-sized particles from the surface without excess dust buildup in the atmosphere, thus improving the agreement with some of the observations without diverging from the observed column opacities.