ABSTRACT Using high-resolution hydrodynamical cosmological simulations, we conduct a comprehensive study of how tidal stripping removes dark matter and stars from galaxies. We find that dark matter is always stripped far more significantly than the stars-galaxies that lose ∼80% of their dark matter, typically lose only 10% of their stars. This is because the dark matter halo is initially much more extended than the stars. As such, we find that the stellar-to-halo size-ratio (measured using reff/rvir) is a key parameter controlling the relative amounts of dark matter and stellar stripping. We use simple fitting formulae to measure the relation between the fraction of bound dark matter and the fraction of bound stars. We measure a negligible dependence on cluster mass or galaxy mass. Therefore, these formulae have general applicability in cosmological simulations, and are ideal to improve stellar stripping recipes in semi-analytical models, and/or to estimate the impact that tidal stripping would have on galaxies when only their halo mass evolution is known.