The ozone concentration in the tropical stratosphere peaks at 26 km, protecting life from harmful ultraviolet light without poisoning it. Climate models reproduce this peak, but textbook explanations yield errors of 10 km. Simplifying the well-understood sources and sinks of ozone, we develop a theory explaining that tropical ozone peaks where its dominant sink transitions from damping of atomic oxygen aloft (mainly via catalytic chemistry) to damping of ozone below (mainly via transport).