Among tetrapods, only bats, birds, and pterosaurs have evolved powered flight independently by flapping their wings. Each group optimizes different aspects of flight performance. Pterosaurs have a unique wing anatomy where most of the wing membrane is supported by one hyperelongated fourth finger. The flight performances of pterosaurs are investigated using 10 species with a wide spectrum of size, where the wingspan ranges from 0.4 m to 10.4 m. Thus the largest pterosaur in our study weighs about 5600 times more than the smallest species, and the longest wingspan is 26 times the shortest. Our aim is to search for a uniform set of aerodynamic constraints across this wide spectrum. Pterosaurs had wings of low loading and high aspect ratio. The wings are attached to the legs, which were projected horizontally to help adjust the membrane. The wing tip appears to be more rounded to avoid stalling than is usually reconstructed. Helicopter momentum stream tube theory was used to minimize the complexities of animal physiology. The power curves, displaying maximum and minimum level flight speeds, were calculated from the computer program (ANFTPWR). The power profile shows that for the four smaller species (mass <0.3 kg), including Eudimorphodon, Pterodactylus, Rhamphorhynchus, and Dorygnathus, the available aerobic power (Pa) exceeds the required power at zero speed, and they are evidently capable of extended flapping flight. Tapejara may also be able to flap, but may depend on low-level anaerobic power. Nyctosaurus and Dsungaripterus appear to be capable of steady level flight at power Pa, but within a limited speed range. The giant Cretaceous pterodactyls such as Pteranodon and Quetzalcoatlus were excellent soarers with low sinking speeds. The air speed for best gliding depends on size, increasing proportionate to mass and wing loading, from as low as 4 m/s for Eudimorphodon to 14 m/s for Quetzalcoatlus. Although small pterosaurs apparently had sufficient available power for taking off from the ground, larger pterodactyls such as Pteranodon and Quetzalcoatlus were limited in their takeoff capabilities. They would depend on brief periods of high anaerobic power generation for a running takeoff with a moderate headwind and thermal updrafts. For large pterodactyls, taking off from a high cliff may have been more cost effective than a ground takeoff.