At what altitude does atmospheric density drop to about 1% of its sea-level value?

32 kilometers up

The dramatic thinning of the atmosphere is quantifiable, illustrating why higher altitudes mark the transition to space. By the time an ascending vehicle reaches an altitude of 32 kilometers above the surface, the density of the air has already decreased to roughly 1% of the density experienced at sea level. This rapid decline means that by the time the Kármán line at 100 kilometers is reached, the remaining atmosphere is an infinitesimally small fraction of the ground-level density. This stark reduction in molecules directly correlates with the physical impossibility of sustaining flight using conventional aerodynamic principles, as there are simply not enough air molecules interacting with the wings to generate necessary lift, even at high speeds.