Cold pools of air, which are formed by evaporating precipitation, play a critical role in the triggering of new precipitation, especially in unorganized tropical convection. Despite their recognized importance, little effort has been devoted to building simple models of their dynamics. Here, analytical expressions are derived for the radius, height, and buoyancy of a cold pool as a function of time. These expressions give a simple equation for the radius of a cold pool when it terminates by ceasing to be cold. The terminal radius of a cold pool is relatively insensitive to its initial conditions, with a typical maximum radius of about 14 times the initial radius, give or take a factor of two. The terminal time of a cold pool, on the other hand, can vary over orders of magnitude depending on its initial potential and kinetic energy. These predictions are validated against large-eddy simulations.