The Strahler stream order assigned to a particular stream segment depends on the scale of the topographic map used in ordering the stream network. However, the Horton‐Strahler bifurcation ratio of stream number, stream length ratio, and stream concavity are found to be independent of map scale. The coefficients in Horton's laws obtained from a map system of one scale can be transferred to a map system of another scale if the stream order difference between the two map systems is given. Yang's theoretical and equilibrium longitudinal stream bed profiles are shown to be independent of map scale and can be compared favorably with an actual profile obtained from a topographic map of any scale.