Solar cells based on the organic–inorganic tri-halide perovskite family of materials have shown significant progress recently, offering the prospect of low-cost solar energy from devices that are very simple to process. Fundamental to understanding the operation of these devices is the exciton binding energy, which has proved both difficult to measure directly and controversial. We demonstrate that by using very high magnetic fields it is possible to make an accurate and direct spectroscopic measurement of the exciton binding energy, which we find to be only 16 meV at low temperatures, over three times smaller than has been previously assumed. In the room-temperature phase we show that the binding energy falls to even smaller values of only a few millielectronvolts, which explains their excellent device performance as being due to spontaneous free-carrier generation following light absorption. Additionally, we determine the excitonic reduced effective mass to be 0.104me (where me is the electron mass), significantly smaller than previously estimated experimentally but in good agreement with recent calculations. Our work provides crucial information about the photophysics of these materials, which will in turn allow improved optoelectronic device operation and better understanding of their electronic properties.