This paper critically compiles all published cases of established or putative calcium action potentials (or ultrafast calcium waves) where their speeds are known and are not limited by intercellular delays. The 127 cases include data from neurons or nerve nets within systems that range from cnidaria, ctenophores, molluscs, crustaceans, worms, echinoderms and tunicates up to mammalian brains; from muscle cells within organisms that range from Beröe, Cestum, moths, a crab, molluscs, a tunicate, frogs, chick embryos and turtles up to mammalian hearts; from epithelia in cnidaria and tunicates; even from a dinoflagellate and an insectivorous plant as well as reconstituted heart strands. They reveal a restriction to values of about 10-40 cm/sec at 20 degrees C and comparable restrictions at other temperatures. Moreover -unlike the speeds of sodium action potentials -the speeds of calcium ones are unrelated to cell diameter, at least over the available range of about 0.1 to 30 microns. Why do calcium action potentials have such fixed propagation speeds? Perhaps evolution has driven them to be the fastest waves of calcium influx which avoid subsurface poisoning.