According to Robert Matthews of BBC Focus Science and Technology, a typical balloon can travel approximately 6 miles into the atmosphere before popping. How far it travels horizontally depends on the direction and strength of the wind.
The atmosphere becomes less dense at higher altitudes, which reduces the force pushing in on the balloon. As a result, a helium-filled balloon slowly expands as it rises. Because balloons are thin and relatively weak, they eventually rupture and slowly fall to the ground. Specially designed balloons, however, can reach much greater heights. A balloon designed at the Institute of Space and Astronautical Science rose 33 miles.