Disease spread has traditionally been described as a traveling wave of constant velocity. However, aerially dispersed pathogens capable of long-distance dispersal often have dispersal gradients with extended tails that could result in acceleration of the epidemic front. We evaluated empirical data with a simple model of disease spread that incorporates logistic growth in time with an inverse power function for dispersal. The scale invariance of the power law dispersal function implies its applicability at any spatial scale; indeed, the model successfully described epidemics ranging over six orders of magnitude, from experimental field plots to continental-scale epidemics of both plant and animal diseases. The distance traveled by epidemic fronts approximately doubled per unit time, velocity increased linearly with distance (slope ~(1/2)), and the exponent of the inverse power law was approximately 2. We found that it also may be possible to scale epidemics to account for initial outbreak focus size and the frequency of susceptible hosts. These relationships improve understanding of the geographic spread of emerging diseases, and facilitate the development of methods for predicting and preventing epidemics of plants, animals, and humans caused by pathogens that are capable of long-distance dispersal.