The risk of a doomsday scenario in which high-energy physics experiments trigger the destruction of the Earth has been estimated to be minuscule. But this may give a false sense of security: the fact that the Earth has survived for so long does not necessarily mean that such disasters are unlikely, because observers are, by definition, in places that have avoided destruction. Here we derive a new upper bound of one per billion years (99.9% confidence level) for the exogenous terminal-catastrophe rate that is free of such selection bias, using calculations based on the relatively late formation time of Earth.