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We present a new scaling law to predict the loss of atmosphere from planetary collisions for any speed, angle, impactor mass, target mass, and body compositions, in the regime of giant impacts onto broadly terrestrial planets with relatively thin atmospheres. To this end, we examine the erosion caused by a wide range of impacts, using 3D smoothed particle hydrodynamics simulations with sufficiently high resolution to directly model the fate of low-mass atmospheres around 1% of the target's mass. Different collision scenarios lead to extremely different behaviours and consequences for the planets. In spite of this complexity, the fraction of lost atmosphere is fitted well by a power law. Scaling is independent of the system mass for a constant impactor mass ratio. Slow atmosphere-hosting impactors can also deliver a significant mass of atmosphere, but always accompanied by larger proportions of their mantle and core. Different Moon-forming impact hypotheses suggest that around 10 to 60% of a primordial atmosphere could have been removed directly, depending on the scenario. We find no evident departure from the scaling trends at the extremes of the parameters explored. The scaling law can be incorporated readily into models of planet formation.