Stalagmites come in a variety of shapes, with sizes ranging from centimeters to meters. Despite their intriguing regularity and their importance for paleoclimate studies, a theoretical description of their form has been lacking. We have developed an analytic theory that provides an explicit formula for the shapes of steadily growing stalagmites, and characterizes the variety of observed shapes in terms of a single parameter. Our results provide a unified perspective on different numerical approaches to stalagmite growth, and make connections to theories of stalactite growth as well. The results can also be used to help infer paleoclimatic information derived from isotope measurements.