The problem of evaporating droplet ballistics in a uniform gas stream is solved analytically. The main regularities of the process are obtained as the approximate solution of the governing differential equations of the droplet motion and evaporation in a practically important range of the determinant parameters. The equations reflect convective evaporation enhancement and transiency of droplet diameter and relative velocity, which have an influence on both droplet motion and evaporation. Formulas for droplet lifetime and path length, the moving droplet evaporation law, and the law of evaporating droplet motion are obtained in an implicit form. Found dependences provide the possibility to analyze theoretically the droplet behavior in a stream. The found relationships show that the convective enhancement of the evaporation reduces the droplet path length up to 3 times, and lifetime up to 9 times. Two main regimes of the droplet evaporation ballistics are revealed: the dynamic evaporation and dynamic acceleration, which occur depending on the ballistic criterion value. The power-mode evaporation law is realized only within the dynamic evaporation regime. Calculations testify to the strong influence of the evaporation on a droplet motion. An approximate expression for the vapor mass production history along droplet trajectory is obtained. The obtained relationships have an acceptable error in a wide range of the found criteria. They allow significant simplification of the quantitative description of evaporation ballistics in sprays and are applicable to various engineering problems. The results are limited to the cases when the evaporation rate may be expressed by some effective evaporation constant value.