Little is known about how individual cells sense the macroscopic geometry of their tissue environment. Here we explore whether long-range electrical signaling can convey information on tissue geometry to influence electrical dynamics of individual cells. First, we studied an engineered electrically excitable cell line where all voltage-gated channels were known. Cells grown in patterned islands of different shapes showed remarkably diverse firing patterns, including regular spiking, period-doubling alternans, and arrhythmic firing. A spatially resolved Hodgkin-Huxley numerical model quantitatively reproduced these effects, showing how the macroscopic geometry affected the single-cell electrophysiology via gap junction-mediated electrical coupling. Qualitatively similar geometry dependent dynamics were observed in human induced pluripotent stem cell (iPSC)-derived cardiomyocytes. The cardiac results urge caution in translating observations of arrhythmia in vitro to predictions in vivo where the tissue geometry is very different. These findings establish that tissue geometry is a fundamental determinant of dynamical stability in excitable cells.