Collective movement is important during emergencies such as natural disasters or terrorist attacks, when rapid egress is essential for escape. The development of quantitative theories and models to explain and predict the collective dynamics of pedestrians has been hindered by the lack of complementary data under emergency conditions. Collective patterns are not restricted to humans, but have been observed in other non-human biological systems. In this study, a mathematical model for crowd panic is derived from collective animal dynamics. The development and validation of the model is supported by data from experiments with panicking Argentine ants (Linepithema humile). A first attempt is also made to scale the model parameters for collective pedestrian traffic from those for ant traffic, by employing a scaling concept approach commonly used in biology.