Quick responses to fast changes in the environment are crucial in animal behaviour and survival,for example to seize prey, escape predators, or negotiate obstacles. Here, we study the ‘simpleresponse time’ that is the time elapsed between receptor stimulation and motor activation astypically shown in escape responses, for mobile organisms of various taxa ranging from bacteria tolarge vertebrates. We show that 95% of these simple response times lie within one order ofmagnitude of the overall geometric mean of about 25 ms, which is similar to that of a well-studiedsensory time scale, the inverse of the critical flicker fusion frequency in vision, also lying withinclose bounds for all the organisms studied. We find that this time scale is a few times smaller thanthe minimum time to move by one body length, which is known to lie also within a relativelynarrow range for all moving organisms. The remarkably small 102-fold range of the simpleresponse time among so disparate life forms varying over 1020-fold in body mass suggests that it isdetermined by basic physicochemical constraints, independently on the structure and scale of theorganism. We thus propose first-principle estimates of the simple response and sensory time scalesin terms of physical constants and a few basic biological properties common to mobile organismsand constraining their responses.