The geometry of the simpler types of graptolite stipes can be quantified by assuming them to consist of stacked cylinders representing the thecal tubes. It can be shown that specification of any three characters, for example, thecal inclination, thecal spacing, and stipe width, effectively defines the others (thecal overlap, thecal length and width, thecal “density”); hence the parameters commonly used in the definition of species are not independent. Variation within and between species can be represented by three-character plots. The effects of altering the apertural angle from 90° on such characters as thecal spacing can also be represented geometrically. If thecae are considered as cones rather than cylinders, it follows that as stipe width increases, thecal curvature will describe a sine curve if the thecae are to remain in contact; this observation is matched on real graptolites. Thecal curvature beyond 90° to the dorsal wall is generally impossible without thecae detaching from their neighbors to produce thecal isolation. Growth of thecae along a stipe can be represented graphically. Computer fits to growth curves for five dichograptids show that they can be closely described by an exponential decrease in growth increments along the stipe, and that this model is more accurate than two possible alternatives.