During chemotaxis and phototaxis, sperm, algae, marine zooplankton, and other microswimmers move on helical paths or drifting circles by rhythmically bending cell protrusions called motile cilia or flagella. Sperm of marine invertebrates navigate in a chemoattractant gradient by adjusting the flagellar waveform and, thereby, the swimming path. The waveform is periodically modulated by Ca(2+) oscillations. How Ca(2+) signals elicit steering responses and shape the path is unknown. We unveil the signal transfer between the changes in intracellular Ca(2+) concentration ([Ca(2+)](i)) and path curvature (?). We show that ? is modulated by the time derivative d[Ca(2+)](i)/dt rather than the absolute [Ca(2+)](i). Furthermore, simulation of swimming paths using various Ca(2+) waveforms reproduces the wealth of swimming paths observed for sperm of marine invertebrates. We propose a cellular mechanism for a chemical differentiator that computes a time derivative. The cytoskeleton of cilia, the axoneme, is highly conserved. Thus, motile ciliated cells in general might use a similar cellular computation to translate changes of [Ca(2+)](i) into motion.