Vocal reaction times were measured for targets presented at three distances from fixation. The targets were preceded by a cue, and the time interval between the cue and the target (stimulus-onset asynchrony; SOA) was varied. For each peripheral distance, the reaction time function initially declined as SOA was increased and then reached asymptote. The further the target from fixation, the longer the SOA at which the function reached asymptote. The asymptotic SOA values were taken as a measure of the time it takes attention to reach a given target. Comparisons of these values for the three peripheral distances permitted estimating the velocity of attention movements. These measurements suggest that when summoned by a peripheral cue, attention travels through space at a constant velocity of about 1 degree per 8 msec.