Geochemical and isotopic observations constrain the timing, temperature and pressure of Earth's formation. However, to fully interpret these observations, we must know the degree of mixing and equilibration between metal and silicates following the collisions that formed the Earth. Recent fluid dynamical experiments provide initial estimates of this mixing, but they entirely neglect the inertia of planet-building impactors. Here we use laboratory experiments on the impact of a dense liquid volume into a lighter liquid pool to establish scaling laws for mixing as a function of the impactor speed, size, density and the local gravity. Our experiments reproduce the cratering process observed in impact simulations. They also produce turbulence down to small scales, approaching the dynamical regime of planetary impacts. In each experiment, we observe an early impact-dominated stage, which includes the formation of a crater, its collapse into an upward jet, and the collapse of the jet. At later times, we observe the downward propagation of a buoyant thermal. We quantify the contribution to mixing from both the impact and subsequent thermal stage. Our experimental results, together with our theoretical calculations, indicate that the collapse of the jet produces much of the impact-induced mixing. We find that the ratio between the jet inertia and the impactor buoyancy controls mixing. Applied to Earth's formation, we predict full chemical equilibration for impactors less than 100 km in diameter, but only partial equilibration for Moon-forming giant impacts. With our new scalings that account for the impactor inertia, the mass transfer between metal and silicates is up to twenty times larger than previous estimates. This reduces the accretion timescale, deduced from isotopic data, by up to a factor of ten and the equilibration pressure, deduced from siderophile elements, by up to a factor of two.